CAT 2023 Linear and Quadratic Equations Question (Hard)

Question

The equation has as one of its roots. If the other two roots are real, what is the minimum possible non-negative integer value of ?

Accepted Answer

Step 1 We are given the cubic equation x 3 2r 1 x 2 4r -1 x 2 0 and that is a root. So divide the cubic by . By synthetic division Coefficients of 1, , , 2 Carry out division by 1 2 First, 1 comes down. Multiply 1 by Multiply by Then Multiply by Then Thus, quotient So x 3 dots x 2 x 2 2r -1 x 1 We a

CAT 2023

Quantitative

Linear and Quadratic Equations

Hard

The equation $x^3 + (2r+1)x^2 + (4r−1)x+2=0$ has $-2$ as one of its roots. If the other two roots are real, what is the minimum possible non-negative integer value of $r$ ?

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