Question

If a and b are the zeros of the quadratic
polynomial kx2 -5x + 4 such that (a + b)2 = 25
then the value of k is:
a​

Answer 1

$\footnotesize \blue ➱\tt{ \: Find:- }$

$\footnotesize ➱ \tt\blue{ \: Value \: of \: k }$

$\:$

$\footnotesize \blue ➱\tt{ \: Given:- }$

$\footnotesize ➱ \tt\blue{ \: a \: and \: b \: are \: the \: zeroes }$

$\footnotesize ➱\tt \blue{ \: {(a+b)}^{2} = 25}$

$\:$

$\footnotesize \blue ➱\tt{ \: Solution:- }$

$\:$

$\footnotesize \blue ➱\tt{ \: {kx}^{2} - 5x + 4 }$

$\:$

$\footnotesize \blue ➱ \tt{ \: Sum \: of \: zeroes(a+b) = \: } \blue{ \frac{ - b}{a} }$

$\footnotesize \blue ➱ \tt{ \: Sum \: of \: zeroes(a+b) = \: } \blue{ \frac{-(-5)}{k} }$

$\footnotesize \blue ➱ \tt{ \: Sum \: of \: zeroes(a+b) = \: } \blue{ \frac{5}{k} }$

$\:$

$\footnotesize \blue ➱\tt{ {(a+b)}^{2} = 25}$

$\blue ➱ \tt{ \: (\frac{5}{k})^{2} = \: } \blue{ 25 }$

$\blue ➱ \tt{ \: \frac{25}{ {k}^{2} } = \: } \blue{ 25 }$

$\:$

$\footnotesize ➱ \tt\blue{ \: Cross \: Multiplication }$

$\:$

$\footnotesize\blue ➱ \tt{ \: 25 = \: } \blue{ 25{k}^{2} }$

$\blue ➱ \tt{ \: \frac{25}{25} = \: } \blue{ {k}^{2}}$

$\blue ➱ \tt{ \cancel{ \: \frac{25}{25}} = \: } \blue{ {k}^{2}}$

$\footnotesize\blue ➱ \tt{ \: 1 = \: } \blue{ {k}^{2}}$

$\footnotesize\blue ➱ \tt{ \: \sqrt{1} = \: } \blue{ k}$

$\boxed{ \boxed{\footnotesize\blue ➱ \tt{ \: 1 = \: } \blue{ {k}}}}$