CAT 2023 Slot 1 Solved Paper

Given that -2 is a root of the given cubic equation.
⇒ Dividing the given equation by (x+2), Using the Horners method of synthetic division:
coefficient of x2 is 1 , and coefficient of x is (2r+1)−2=2r−1 and the constant term =(4r−1)−2(2r−1)=1.
⇒ The quadratic obtained by dividing the cubic =x2+(2r−1)x+1=0, Since, this equation has 2 real
roots ⇒ Discriminant should be greater than 0
⇒(2r−1)2>4⇒2r−1>2 or 2r−1<−2⇒r>3∕2 or r<−1∕2.
⇒ Minimum possible non-negative integer value of r is 2 .