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Class 10 Sum and Product of Roots — practice questions with answers

Algebra — Quadratics · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. For the quadratic equation x² - 5x + 6 = 0, what is the sum of its roots?
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Answer: A) 5
Sum of roots = = = 5.
2. The sum of the roots of 5x² - 10x + 1 = 0 is:
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Answer: C) 2
Sum = = = = 2.
3. The roots of a quadratic equation are alpha and beta.
Given alpha + beta = 9 and alpha x beta = 14.
What is the value of alpha² + beta²?
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Answer: B) 53
alpha² + beta² = (alpha + beta)² - 2 alpha beta = 81 - 28 = 53.
4. If alpha and beta are roots of x² - 5x + 6 = 0, then the equation whose roots are alpha + 1 and beta + 1 is:
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Answer: A) x² - 7x + 12 = 0
Roots 2 and 3 become 3 and 4. New sum = 7, new product = 12: x² - 7x + 12 = 0.
5. Priya frames a quadratic equation x² - bx + c = 0 in which one root is 5 more than the other, and the product of the roots is 36.
What is the smaller root?
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Answer: A) 4
Let roots r and r+5 with r(r+5) = 36, i.e. r² + 5r - 36 = 0 = (r+9)(r-4). Positive root r = 4 (other root 9, product 36). Smaller root = 4.
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