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(kx)2 + kx + 1 = …

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(kx)2 + kx + 1 = (-4x)2 - x

Posted by Anurag Khobragade 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

We have,
{tex}kx^2 + kx + 1 = -4x^2 - x{/tex}
{tex}\Rightarrow{/tex} {tex}kx^2 + 4x^2 + kx + x + 1 = 0{/tex}
{tex}\Rightarrow{/tex}{tex} (k + 4)x^2 + (k + 1)x + 1 = 0{/tex}
Here, a = k + 4, b = k + 1 and c = 1
{tex}\therefore{/tex} {tex}D = b^2 - 4ac{/tex}
= (k + 1)² - 4 {tex}\times{/tex} (k + 4) {tex}\times{/tex} (1)
{tex}= k^2 + 1 + 2k - 4k - 16{/tex}
{tex}= k^2 - 2k - 15{/tex}
{tex}\Rightarrow{/tex} {tex}D = k^2 - 2k - 15{/tex}
The given equation will have real and equal roots, if
D = 0
{tex}\Rightarrow{/tex} {tex}k^2 - 2k - 15 = 0{/tex}
{tex}\Rightarrow{/tex}{tex} k^2 - 5k + 3k - 15 = 0{/tex}
{tex}\Rightarrow{/tex} k(k - 5) + 3(k - 5) = 0
{tex}\Rightarrow{/tex} (k - 5)(k + 3) = 0
{tex}\Rightarrow{/tex} k - 5 = 0 or k + 3 = 0
{tex}\Rightarrow{/tex} k = 5 or k = -3

0Thank You

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