Question

If $\alpha ,\beta$ be the zeros of the polynomial $2x^2+5x+k$ such that ${\alpha }^2+{\beta }^2+\alpha \beta =\frac{21}{4}$ then k = ?

(a) 3 (b) -3 (c) -2 (d) 2

Answer 1

: α and β are zeroes of polynomial
2x² + 5x + k

We know that $\alpha +\beta =\frac{-b}{a}$ and $\alpha .\beta =\frac{c}{a}$
$\to$ α+β = , αβ =

⇒ (α+β)² = ()²

⇒ α²+ β²+ 2αβ =
⇒ α²+ β²+ αβ+ αβ =

$\to$ +

$\Rightarrow$

$\Rightarrow \frac{k}{2}=\frac{4}{4}$

$\Rightarrow \frac{k}{2}=1$

$\Rightarrow k=2$

Ans. $\Rightarrow k=2$