Question

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

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:k=\frac{-1-2\sqrt{2}}{4}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given : }} \\ \tt: \implies( x + 2) \: is \: factor \\ \\ \tt: \implies {kx}^{2} - \sqrt{2} x + 1 = 0 \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies Value \: of \: k =?$

• According to given question :

$\tt \circ \: x = - 2\\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies p(x) \to {kx}^{2} - \sqrt{2} x + 1 = 0 \\ \\ \tt: \implies p( - 2) \to k \times {( - 2)}^{2} - \sqrt{2} ( - 2) + 1 = 0 \\ \\ \tt: \implies k \times 4 + 2 \sqrt{2} + 1 = 0 \\ \\ \tt: \implies 4k + 2 \sqrt{2} + 1 = 0 \\ \\ \tt: \implies 4k = - 1 - 2 \sqrt{2} \\ \\ \green{\tt: \implies k = \frac{ - 1 - 2 \sqrt{2} }{4} } \\ \\ \green{\tt \therefore Value \: of \: k \: is \: \frac{ - 1 - 2 \sqrt{2} }{4} }$

Answer 2

✯✯ QUESTION ✯✯

Find the value of k if x+2 is a factor of kx²-√2x+1..

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✰✰ ANSWER ✰✰

$\longrightarrow\tt{x+2=0}$

$\longrightarrow\tt{x=0-2}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{x}\orange{=}\purple{-2}}}$

Putting x = -2

$\longrightarrow\tt{{kx}^{2}-\sqrt{2x}+1=0}$

$\longrightarrow\tt{k{(-2)}^{2}-\sqrt{2}(-2)+1=0}$

$\longrightarrow\tt{k(4)-\sqrt{2}(-2)+1=0}$

$\longrightarrow\tt{4k+2\sqrt{2}+1=0}$

$\longrightarrow\tt{4k=0-1-2\sqrt{2}}$

$\red\longmapsto\:\small\underline{\boxed{\bf\green{k}\orange{=}\blue{\dfrac{-1-2\sqrt{2}}{4}}}}$

➥So, Value of k = $\tt\dfrac{-1-2\sqrt{2}}{4}$