JEE PYQ: Quadratic Equation Question 24
Question 24 - 2020 (06 Sep Shift 2)
If $\alpha$ and $\beta$ are the roots of the equation $2x(2x + 1) = 1$, then $\beta$ is equal to:
(1) $2\alpha(\alpha + 1)$
(2) $-2\alpha(\alpha + 1)$
(3) $2\alpha(\alpha - 1)$
(4) $2\alpha^2$
Show Answer
Answer: (2)
Solution
Let $\alpha$ and $\beta$ be the roots of the given quadratic equation,
$2x^2 + 2x - 1 = 0$ …(i)
Then, $\alpha + \beta = -\frac{1}{2} \Rightarrow -1 = 2\alpha + 2\beta$
and $4\alpha^2 + 2\alpha - 1 = 0$ [$\because \alpha$ is root of eq. (i)]
$\Rightarrow 4\alpha^2 + 2\alpha + 2\alpha + 2\beta = 0 \Rightarrow \beta = -2\alpha(\alpha + 1)$
BETA
