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QUADRATIC EQUATIONS, , , , , , , , SECTION A: (1 MARK), 1. (-2,3), Find the value of .| 6+ ¥6+ V6+4+°-:- (CBSE BOARD 2016), 2. A polygon of n sides has = diagonals. How many sides has a polygon with 54 (12), diagonals?, 3. Find the roots of the equation ax’ + a = a°x + x (a,~), a, SECTION B: (2 MARKS), 4. Solveforx: V3x2+x+5=x-3 (CBSE BOARD 2012) (-4-), 5. Find the value of p for which x” + 5px + 16 = 0 has no real roots. anes, 5 5, 6. One day, | asked the son of my close friend about his age. The child replied in a (x’-8x+7=0), different way. He said, “One year ago, my dad was 8 times as old as me and now, his age is equal to square of my age.” Represent this situation in the form of a, quadratic equation. (CBSE BOARD 2007), 7. Find the value of p for which the quadratic equation 4x2 — 3px + 9 = 0 has real (p=4or, roots. ps —4), 8. If y=1 is acommon root of the equations ay2 + ay +3 =O and y2+y+b=0, (3), , find ab. (CBSE BOARD 2012), , , , SECTION C: (3 MARKS), , 9., , 10., , 11., , 12., , 13., , Solve for x: 2 %*3 = 65(2"-2) +122 (CBSE BOARD 2012), , Solve for x: x? + 5x—(a* +a—6) =0., Solve for x: 9x” — 9(a + b)x + (2a” + Sab + 2b’) = 0., , ~=2,x#a,b., , Solve for x: —— +, x—b x-a@, , (CBSE BOARD 2004), , 7 = 4-45 (x# 0,b#0,x #0) (CBSE BOARD 2005), , , , Solve for x :, atbt+c, , (-3,3), [-(a+3),(a-2)], 2a+ba+2b, , : a, , [ (arb), , , , , , , , (-a , -b)

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9 ot, 14, Solve for x: fe + BS =22 (x#0,1) (CBSE BOARD 2000) Sis!, , , , SECTION D: (4 MARKS), , 15. The numerator of a fraction is 1 less than the denominator. If 3 is added to each of (3/4), the numerator and denominator, the fraction is increased by 3/28. Find the fraction., (CBSE BOARD 2016), , 16. The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples. (14,21), (CBSE BOARD 2016), , 17. The total cost of a certain length of a piece of cloth is 8200. If the piece was 5m (20m,%10), longer and each meter of cloth costs %2 less, the cost of the piece would have, remained unchanged. How long is the piece and what is its original rate per meter?, (CBSE BOARD 2012), 18. If the roots of the quadratic equation x” + 2px + mn = 0 are real and equal, show that, the roots of the quadratic equation x” — 2(m + n)x + (m? + n? + 2p”) = 0 are also equal., (CBSE BOARD 2008), 19. Atank can be filled by one pipe in x minutes and emptied by another pipe in (x + 5) (7 hours), minutes. Both the pipes when opened together can fill the empty tank in 16.8, , minutes. Find x. (EXEMPLAR PROBLEM), 20. Solve for x:5**'+5?-*= 126 (2,-1), 21. If the roots of the equation (a — b) x” + (b— c) x + (c—a) = O are equal,, prove that 2a=b+c. (EXEMPLAR PROBLEM), 22. ee a —* “1, Solve for x : + Sat Ga 0;x # 3,-5 (-1), , 23. Students of class X collected 318000. They wanted to divide it equally among a (30), certain number of students residing in slum area. When they started distributing the, amount, 20 more students from the nearby slums also joined. Now each student get, 240 less., , (a) Find the number of students living in the slum., (b) Which value is depicted by the students? (CBSE BOARD 2013), , 24. Out of anumber of saras birds , one fourth of the number are moving about in lots, (576), 1/9 th coupled with % th as well as 7 times the square root of the number move ona, hill, 56 birds in vakula trees. What is the total number of birds? (CBSE BOARD 2004), , 25. Att minutes past 2 p.m. the time needed by the minutes hand of a clock to show 3 (14), p.m. was found to be 3 minutes less than t2/4 minutes. Find t., (EXEMPLAR PROBLEM))