Test Details

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Polynomials

Nov 27, 4:00 PM

60 minutes

Nov 28, 5:00 PM

34.0 marks

MCQ

21 questions

Sheeja N

P. G, B.Ed in Maths

Class Details

English

Mathematics

Class 10

English

Mathematics

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Question Text

Question 3 :
Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients.$49x^2-81$

Question 4 :
Find the value of a & b, if  $8{x^4} + 14{x^3} - 2{x^2} + ax + b$ is divisible by $4{x^2} + 3x - 2$

Question 5 :
Find the Quotient and the Remainder when the first polynomial is divided by the second.$-6x^4 + 5x^2 + 111$ by $2x^2+1$

Question 6 :
What must be subtracted from $4x^4 - 2x^3 - 6x^2 + x - 5$, so that the result is exactly divisible by $2x^2 + x - 1$?

Question 7 :
State whether True or False.Divide: $x^2 + 3x -54 $ by $ x-6 $, then the answer is $x+9$.

Question 8 :
Find the expression which is equivalent to : $\displaystyle \frac { { x }^{ 3 }+{ x }^{ 2 } }{ { x }^{ 4 }+{ x }^{ 3 } } $?

Question 9 :
Simplify:Find$\ x(x + 1) (x + 2) (x + 3) \div  x(x + 1)$

Question 10 :
The remainder when$4{a^3} - 12{a^2} + 14a - 3$ is divided by $2a-1$, is

Question 11 :
The value of $m$ for which the equation $\dfrac { a }{ x+a+m } +\dfrac { b }{ x+b+m } =1$ has roots equal in magnitude but opposite in sign is

Question 12 :
If $a, b$ are the roots of $x^2 + px + 1 = 0$ and $c, d$ are the roots of $x^2 + qx + 1 = 0,$ the value of $E = (a - c)(b - c)(a + d) ( b + d)$ is

Question 13 :
If $\alpha$ and $\beta$ are the zeros of the polynomial $f(x)=5x^2+4x-9$ then evaluate the following: $\alpha^4-\beta^4$

Question 14 :
If one factor of the polynomial $x ^ { 3 } + 4 x ^ { 2 } - 3 x - 18$ is $x + 3,$ then the other factor is

Question 15 :
What must be added to $f(x)=4x^4+2x^3+2x^2+x-1$ so that the resulting polynomial is divisible by $g(x)=x^2+2x-3$

Question 17 :
State whether True or False.Divide: $16 + 8x + x^6-8x^3 -2x^4+ x2 $ by $ x+ 4-x^3$, then the answer is $-x^3+x+4$.

Question 18 :
If the polynomial $(x + 1)^{2015} - x^{2015} - 1$ is divided by $(x + x^2 + x^3)$, then the remainder is

Question 19 :
When ${ x }^{ 2 }-2x+k$ divided the polynomial ${ x }^{ 2 }-{ 6x }^{ 3 }+16{ x }^{ 2 }-25x+10$ the reminder is (x+a), the value of is

Question 21 :
Total number of polynomials of the form ${ x }^{ 3 }+a{ x }^{ 2 }+bx+c$ that are divisible by ${ x }^{ 2 }+1$, where $a,b,c\in \left\{ 1,2,3,......10 \right\} $ is equal to

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