Question

1. Determine the value of 'k' such that kx2–5x + k = 0 has two equal roots.

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Answer 1

Step-by-step explanation:

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Answer 2

$\mathfrak{\blue{\underline{\underline{Question}}}}$

Determine the value of 'k' such that $k{x}^{2} - 5x + k = 0$ has two equal roots.

$\mathfrak{\blue{\underline{\underline{Answer}}}}$

$\boxed{ k = \pm \dfrac{5}{2}}$

$\mathfrak{\blue{\underline{\underline{Step \: By\: Step\: Solution}}}}$

$k{x}^{2} - 5x + k = 0$

Here,

a = k

b = -5

c = k

Given, roots are real and equal.

We know,

$\boxed{D = b^{2} - 4ac = 0}$

$\implies {(-5)}^{2} - 4(k)(k) = 0$

$\implies 25 - 4k^{2} = 0$

$\implies k^{2} = \dfrac{25}{4}$

$\implies k = \sqrt{\dfrac{25}{4}}$

$\implies k = \pm\dfrac{5}{2}$