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Polynomials, Note- E.P Questions are not important for Board Exam but if you want to do for more, practice then you can try…., *E.P.Q= Extra Practice Questions, , Type-1 (Based on basic Polynomial), 1.A polynomial in the following is:, a. 7x2-5√𝑥+√5, , b. t3-2t+1, , c.x2-, , !, , d. %𝑦+5y-1, , "!, , 2. A polynomial of degree n has:, a. only 1 zero, , b. exactly n zeroes, , c. at most n zeroes, , d. more than n zeroes, , 3. Coefficient of x3 is polynomial (x2- 2x + 1)(x2 + 2x +1) is, a. 2, , b. 1, , c. 0, , d. -2, , 4. The degree of the polynomial (x+1)(x2-x-x4+1) is, a. 4, , b. 1, , c. 5, , d. 2, , 5. Degree of the polynomial, , is, , a. Not defined, , b. 6, , c.Not a polynomial, , d. 3(Hots), , 6. Number of points of intersection of the polynomial p(x) = x3 - 8x with x axis, is/are, a. 0, , b. 3, , c. 1, , d. 2

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Type-2 (Number of Zeroes), 7.The number of zeroes of the polynomial as shown in the graph are:, , Y, , X’, , X, , 0, , Y’, a. 3, , b. 4, , c. 1, , d. 2, , 8. In the figure, graph of a polynomial p(x) is given. Find the zeros of p(x)., , Y, 2, , y= p(x), , 1, , X, , X, , 0, , 1, , 2, , 3, , 4, , 5, , 6, 4, , Y’, a. -3, 4, , b. 3, 5, , c. -3, 5, , d. 3, 4

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9. Which of the following is not the graph of a quadratic polynomial?, a., , b., , c., , d., , 10.Zeroes of a polynomial can be determined graphically. Number of zeroes, of a polynomial is equal to number of points where the graph of, polynomial:, a. intersects Y-axis, b. intersects X-axis, c. intersects Y-axis or intersects X-axis, d. None of the above

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Type-3 (Parabola Based & its Graph based), 11.The parabola representing a quadratic polynomial f(x)= ax2 + bx + c, opens upward when:, a. a>0, b. a<0, c. a=1, d. a>1, 12.The parabola representing a quadratic polynomial f(x)= ax2 + bx + c, opens downward when:, a. a<0, b. a>0, c. a<1, d. a>1, 13. The maximum number of zeroes which a quadratic polynomial can have, a. one, , b. two, , c. three, , d. four, , Type-4 (Factorisation & its Zeroes), 14.The zeroes or polynomial x2 – 5x +6 are:, a. -1,0, b. 4,5, c. 3,2, , d. None of these, , 15.For what value of p, 1 is a zero of the polynomial f(x)= 2x2 + 5x – (3p +1)?, a. 3, b. 5, c. 2, d. -1, 16.The zeroes of the polynomial f(x)= x2 - 2√2x – 16 are:, a. √2, -√2, b. 4√2, -2√2, c. -4√2, 2√2, c. 4√2, 2√2, #, , 17.The zeroes of the polynomial f(x)= x2 + x -$ are:, ! #, , a. − %, %, , !, , #, , b. %, -%, , #, , c. 1, − %, , d. 1,, , √#, %, , 18.If the value of a quadratic polynomial p(x) is 0 only at x=-1 and p(-2)= 2,, then value of p(3) is : (Hots), a. 18, b. 9, c. 6, d. 3

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26. If x2 + xy + x = 14, y2 + xy + y = 28 and z = x + y, then the sum of all possible, values of z is: (E.P.Q), a. 7, , b. 6, , c. -1, , 27.If a+b+c=0, then the value of, a.1, , ()*+)!, )+, , +, , (+*-)!, +-, , b. 2, , d. -6, , +, , (-*))!, )-, , is, , c. 3, , d.-3, , 28. If xyz + xy + yz + xz + x + y + z = 384 and x,y,z are positive Integers then, x+y+z is, (E.P.Q), a. 23, , b. 18, , c.20, , d. 35, , 29. If x2 + xy + x= 12 and y2 + xy + y=18, then the value of x+y is: (E.P.Q), a.5 or -6, , b. 3 or 4, , c.5 or 3, , 30.Factors of (3m2 – 2m)(6 - 3m2 + 2m) – 5 are : (Hots), a. (3m + 1)(3m – 5)(m – 1)(m + 1), b. -(3m + 1)(3m – 5)(m – 1)(m + 1), c. (3m - 1)(3m + 5)(m – 1)(m + 2), d. -(3m - 1)(3m + 5)(m – 2)(m + 1), , 31.If 2a2 - 2ab + b2 + 6a + 9 = 0 then (a+b) + ab is. (E.P.Q), a. 1, , b. 2, , c. 3, , d. 4, , d.6 or-3

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32.Let f(x) = x2 - 27x + 196. If f(a)= a, then what is the values of a. (Hots), a. 7, , b. 14, , c.21, , d. 6, , 33.If x=3 + 32/3 +31/3, then the value of x3 – 9x2 + 18x – 12 is., a. 1, , b. 0, , c. -1, , (E.P.Q), , d. 2, , 34.If the zeroes of the polynomial f(x) = k2x2 – 17x + k +2, (k>0) are reciprocal of, each other, then the value of k is, a. 2, , b. -1, , c. -2, , d.1, , 35.If (x+1) is a factor or 2x3 +ax2 +2bx + 1, then find the values of a and b given, that 2a – 3b = 4:, a. x2+ 3x – 2, , b. x2 -2x +3., , c. x2 -3x +2, , d. x2 -3x -2, , 36.The number of zeroes that polynomial f(x)= (x-2)2 +4 can have is: (Hots), a. 1, , b. 2, , c. 0, , d. 3, , 37.If p(x)= ax +b, then zero of p(x) is:, a. a, , b. b, , c., , '), +, , d., , '+, ), , 38.If one of the zeros of polynomial a²x2+x+b2 is – 1 then:, a. a2 +b2=0, , b.a2 +b2 -1 = 0, , c.a2 -b2 +1 = 0, , d.a2 +b2= -1, , 39.if α and β are the zeroes of the polynomial 25x2 – 16, then α2 + β2 is, #%, , a. %., , %., , b. #%, , %., , c. !/, , !/, , d. %.

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Type-5 (Formation of Quadratic Polynomial), 40.The sum and product of zeroes of a quadratic polynomial are 0 and √3, respectively. The quadratic polynomial is:, a. x2 - √3, , b. x2 + √3, , c. x2 – 3, , d. x2 + 3, , !, /, , 41.If the sum of the zeroes of a polynomial is - and product of the zeroes of, the polynomial is -2, then the polynomial is:, !, , a. x2 − / x +2, , c. 6x2 – x+ 12, , !, , b. x2 +/ x -2, , d. 6x2 + x- 12, , 42.A quadratic polynomial whose one zero is 6 and sum of the zeroes is 0, is:, a. x2 -6x +2, c. x2 -6, , b. x2 -36, d. x2 -3, ! !, $ $, , 43.Find a quadratic polynomial, the sum and product of whose zeroes are - , ., a. 4x2 -x +1, c. 4x2 + x +1, , b. 4x2 + x -1, d. None of these, , Type-6(Sum & Product of Roots), 44.If α, β are the zeroes of f(x)= 2x2 + 8x – 8, then:, a. α+ β= αβ, b. α+ β> αβ, c. α+ β< αβ, d. α + β + αβ = 0

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45.If the sum of the zeroes of the polynomial p(x)= (p2 – 23) x2 – 2x – 12 is 1,, then p takes value(s):, a. √23, b. -23, c. 2, d. ±5, , 46.If the zeroes of the polynomial f(x) = k2x2 - 17x + k + 2,(k>0) are reciprocal of, each other than value of k is, a. 2, , b.-1, , c.-2, , d.1, , 47.If α and β are the zeroes of the quadratic polynomial f(t)= t2 – 4t + 3,, then the value of α4β3 + α3β4 is:, a. 104, b. 108, c. 122, d.5, , 48. If sin a and cos b are the roots of ax2 + bx + c=0, then a2 + 2ac = ..., a. C2, , b.– 2ab, , c.b2, , d. 0, , 49.If one of the zeroes of the quadratic polynomial bx2 + cx + d is 0, then the, other zero is:, +, , a. - ), , -, , b. - +, , +, , c. 0, , -, , d. +, , 50.If α, β are the zeroes of the polynomial x2 + 5x + c, and α- β =3, then c=, a. 0, , b. 1, , c. 4, , d. 5, , !, , 51. If one root of the equation x2 + ax + b= 0 is # times the other. Then the, , correct relation among the following is : (Hots), a. 3a2= 16b, , b.16a2=3b, , c. 3a=16b2, , d. 16a=3b2

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!, , !, , 52.If α, β are the zeroes of the polynomial p(x)= x2 – 2x -3, then 1 + 2 is:, %, , !, , a. #, , b. #, , c., , '!, #, , %, , d. − #, , 53.If α, β are zeroes of the polynomial f(x)= x2 – p(x +1) -q, then (α +1)(β +1) =, a. q-1, , b. 1-q, , c. q, , d. 1+q, , 54. If for all the values of a, one zero of the polynomial x2 – 3ax + f(a) is double, of the other zero, then find f(x). (Hots), a.2x, , b. x2, , c. 2x2, , d. 2√𝑥, , 55.If the zeroes of the quadratic polynomial x2 + (a +1)x + b are 4 and -3, then, a-b is:, a. 12, , b. 10, , c. 7, , d. 1, , 56.If α and β be the zeroes of the polynomial p(x)= x2 – 5x + 2, find the value of, !, 1, , !, , + 2 -3αβ., #, , a. − %, , ., , b. − %, , 3, , c. − %, , 4, , d. − %, , 57.If the sum of the zeroes of the quadratic polynomial kx2 +2x +3k is equal to, their product, then k equals:, !, , a. #, , !, , b. − #, , %, , c. #, , %, , d. − #, , 58.If one zero of the polynomial 3x2 +8x +k is the reciprocal of the other, than, value of k is:, a. 3, , b. -3, , !, , c. #, , !, , d. − #

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59.If the zeroes of the quadratic polynomial ax2 + x + a are equal, then value of, a is:, !, , !, , a. %, , b. − %, , !, , c. ± %, , d. ±1, , 60. if one zero of the quadratic polynomial 2x2 -6kx +6x -7 is negative of the, other, then k is equal to:, a. -1, , b. 1, , c. 0, , d. −, , !, %, , 61.If the product of the zeroes of the quadratic polynomial x2 -3az +2a2 -1 is 7,, then a is equal to:, a. ±1, , b. ±, , !, %, , c. ±2, , d. ±3, , 62.If α and β are the zeroes of the polynomial f(x) = x2 – 5x + k such that α – β =, 1, the value of K is – (Hots), a.12, , b. 6, , c. 4, , d.1, )%, , 63. If a,b are the roots of the equation 2x2–5x+16=0 then the value of (+ )!/#, +%, , +() )!/# is : (Hots), !, , ., , a.$, , b. $, , !, , c. #, , ., , d. !%, , 64.If α and β are the root of the polynomial 2x2 + 5x + k such that, αβ =, a. 3, , %!, $, , , then k is, b.-3, , c. -2, , d. 2, , α2 + β 2 +

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65.If one zero of the quadratic polynomial ax2+ 15x + 6 is reciprocal of the, other, then the zeros of the polynomial are:, !, , a. 2 and %, , b. -2 and, , '!, %, , !, , c. 3 and #, , d. -3 and, , '!, #, , Type-6. (Mix Questions), 66.In the polynomial p(x) = x2 - 10x + 2, what number should be taken out as x,, to get the least possible number at p(x). (Hots), a. 10, , b. -5, , c. 0, , d. 5, , !, ", , 67.If x=(3+√8), then ( x2 + 2) will be: (E.P.Q), a 38, , 68.If x=, a.8, , b. 36, , √#*!, %, , c.34, , d. 30, , then the value of 4x3 + 2x2 - 8x+7 is: (E.P.Q), b.10, , c.15, , d. 14, , 69.The minimum value of the polynomial p(x) = 3x2 – 5x + 2 is. (Hots), !, , a.− /, , !, , !, , b. /, , !, , c. !%, , d. − !%, , 70.Number of points of intersection of polynomial f(x) = x3 + 27 and x axis, is/are. (E.P.Q), a. 0, , b. 1, , c. 2, , d. 3

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Answer Key, 1.b, 2.c, 3.c, 4.c, 5.d, 6.b, 7.b, 8.b, 9.d, 10.b, 11.a, 12.a, 13.b, 14.c, 15.c, 16.b, 17.b, 18.a, 19.b, 20.c, 21.b, 22.a, 23.d, 24.b, 25.a, 26.c, , 27.c, 28.c, 29.a, 30.b, 31.c, 32.b, 33.b, 34.a, 35.d, 36.c, 37.c, 38.d, 39.a, 40.b, 41.b, 42.b, 43.c, 44.a, 45.d, 46.a, 47.b, 48.c, 49.b, 50.c, 51.a, 52.d, , 53.b, 54.c, 55.b, 56.c, 57.d, 58.a, 59.c, 60.b, 61.c, 62.b, 63.b, 64.d, 65.b, 66.d, 67.c, 68.b, 69.d, 70.b