JEE Main 2022 · 28 Jun · Shift 2 · Mathematics Q2

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MathematicsSingle correct+4 / -1Question 2 of 90

Let $f(x)$ be a quadratic polynomial such that $f(-2)+f(3)=0$ . If one of the roots of $f(x)=0$ is $-1$ , then the sum of the roots of $f(x)=0$ is equal to :

\dfrac{11}3

\dfrac73

\dfrac{13}3

\dfrac{14}3

Answer and worked solution

Official answer: A

Write $f(x)=a(x+1)(x-r)$ . Then $f(-2)+f(3)=a(2+r)+4a(3-r)=a(14-3r)=0$ , so $r=\frac{14}3$ .

Sum of roots $-1+\frac{14}3=\frac{11}3$ .

(A)

Topics:Roots and coefficients

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JEE Main 2022 · 28 Jun · Shift 2, Mathematics question 2