The quadratic equation x 2 + bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of b 2 + c?

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549 — Easy Use Vieta's relations to express $b$ and $c$ through $a$, form $b^2+c$ as a single expression in $a$, then test which option can equal it for an integer $a$. 1 Sum and product of roots. For $x^2+bx+c=0$ with roots $4a$ and $3a$: $$\begin{aligned} &-b = 4a+3a = 7a \quad	ext{(sum of roots)}\ &\ \ c = (4a)(3a) = 12a^2 \quad	ext{(product of roots)} \end{aligned}$$ 2 Form $b^2+c$. Since $b=-7a$, we get $b^2=49a^2$. $$\begin{aligned} &b^2+c = 49a^2 + 12a^2\ &\Rightarrow\ b^2+c = 61a^2 \end{al

CAT 2019 Slot 2 — QA Question 25

Answer & solution