Question

find the value of k if x+2 is a factor of kx²-√2x+1​
​

Answer 1

$\huge\sf\red{\underline{\underline{Given}}}\::$

$\begin{cases}\sf\gray{( x + 2) \: is \: factor} \\ \sf\gray{{kx}^{2}\: - \: \sqrt{2} x\: +\: 1 \:=\: 0}\end{cases}$

$\huge\sf\blue{\underline{\underline{To\:Find}}}\::$

$\begin{cases}\sf\gray{Value \ of \ k }\end{cases}$

$\huge\sf\pink{\underline{\underline{Solution}}}\::$

$\sf\orange{ATQ}$

$\hookrightarrow \:{\sf{\green{ x \:= \:- 2}}}\\ \\ {\bf{\underline{\blue{As \: we \: know \: that}}}} \\ \\ \leadsto \:\:\:{\sf{\purple{ p(x) \to {kx}^{2} - \sqrt{2} x + 1 = 0 }}} \\ \\ \leadsto \:\:\:{\sf{\green{ p( - 2) \to k \times {( - 2)}^{2} - \sqrt{2} ( - 2) + 1 = 0}}} \\ \\ \leadsto \:\:\:{\sf{\purple{ k \times 4 + 2 \sqrt{2} + 1 = 0}}} \\ \\ \leadsto \:\:\:{\sf{\green{ 4k + 2 \sqrt{2} + 1 = 0}}} \\ \\ \leadsto \:\:\:{\sf{\purple{ 4k = - 1 - 2 \sqrt{2}}}} \\ \\ \leadsto \:\:\:{\sf{\green{ k = \frac{ - 1 - 2 \sqrt{2} }{4} }}} \\ \\ \leadsto \:\:\:{\sf{\pink{ \therefore\: Value \: of \: k \: is \: \frac{ - 1 - 2 \sqrt{2} }{4} }}}$