CAT 2017 Linear and Quadratic Equations Question (Medium)

Question

The minimum possible value of the sum of the squares of the roots of the equation is

Accepted Answer

Step 1 Required expression p q p q 2pq Step 2 Sum and product of roots Sum b a a 3 a 3 Product c a a 5 a 5 --- Step 3 Substitute into formula p q a 3 2 a 5 Expand a 6a 9 2a 10 a 8a 19 --- Step 4 Minimize expression a 8a 19 Complete the square a 8a 16 3 a 4 3 Minimum value 3 occurs when a 4

CAT 2017

Quantitative

Linear and Quadratic Equations

Medium

The minimum possible value of the sum of the squares of the roots of the equation $x^2 + (a + 3)x - (a + 5) = 0$ is

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