Question

if
$\alpha$
,
$\beta$
are the roots of the equation x
${?}^{2}$
-3x+k=0 such that
$\alpha$
=
$2 \beta$
then find k​

Answer 1

${\huge{\pink{\underline{\underline{\purple{\mathbb{\bold{\mathcal{AnSwEr..}}}}}}}}}$

${\large{\blue{\bold{\underline{Given:-}}}}}$

▪︎$\alpha$$\beta$ are two zeroes of :-

$\implies {x}^{2} - 3x + k = 0$

▪︎ $\alpha=2\beta$

${\large{\blue{\bold{\underline{Sum\:of\:zeroes:-}}}}}$

$\implies \alpha + \beta = \frac{ - b}{a} \\ \\ \implies2 \beta + \beta = \frac{ -( - 3)}{1} \\ \\ \implies3 \beta = 3 \\ \\ \implies \beta = \cancel \frac{3}{3} \\ \\ \implies \beta = 1$

${\large{\blue{\bold{\underline{Product\:Of\:Zeroes:-}}}}}$

$\implies \alpha \beta = \frac{c}{a} \\ \\ \implies2 \beta \times \beta = k \\ \\ \implies2 \beta {}^{2} = k \\ \\ \implies2(1) {}^{2} = k \\( \beta = 1) \\ \\ \implies \: k = 2$

☆ Therefore the required value of k is 2.

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