CAT 2022 Linear and Quadratic Equations Question (Medium)

Question

Let and be real numbers. If and are roots of , then equals

Accepted Answer

Step 1 Since the equation is a cubic, it has 3 roots. Let the roots be , , and From Vieta s formula Sum of roots Also, sum of roots So, 1 Step 2 Product of roots From Vieta product So, Hence, 2 Step 3 Substitute equation 1 into 2 So, Multiply both sides by 5 Therefore, Now use this back in equation

CAT 2022

Quantitative

Linear and Quadratic Equations

Medium

Let $r$ and $C$ be real numbers. If $r$ and $-r$ are roots of $5x^3 + cx^2 - 10x + 9 = 0$ , then $c$ equals

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