If x - 1 is factor of p x - x 2 - 2 k x- - 2 - Find the value of k

( x 1) is a factor of p(x ) ⇒ p( x ) =0 ⇒ x 1=0 #160; #160; #160; #160; #160; #160; x=1 ⇒ p( 1)=0 ⇒ p( x) =x ...

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Standard IX

Mathematics

Factor Theorem

If x - 1 i...

Question

If $x - 1$ is factor of $(p x) = x^{2} + 2 k x - \sqrt{2} .$ Find the value of $k$

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Solution

$(x - 1)$ is a factor of $p (x)$
$\Rightarrow p (x) = 0$
$\Rightarrow x - 1 = 0$
$x = 1$
$\Rightarrow p (1) = 0$
$\Rightarrow p (x) = x^{2} + 2 k x - \sqrt{2}$
$\Rightarrow p (1) = 1 + 2 k - \sqrt{2}$
$0 = 1 + 2 k - \sqrt{2}$
$\sqrt{2} - 1 = 2 k$
$\Rightarrow \frac{\sqrt{2} - 1}{2} = k$
Hence, the answer is $\frac{\sqrt{2} - 1}{2} .$

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If x−1 is factor of (px)=x2+2kx−√2. Find the value of k

(x−1) is a factor of p(x)⇒p(x)=0⇒x−1=0 x=1⇒p(1)=0⇒p(x)=x2+2kx−√2⇒p(1)=1+2k−√2 0=1+2k−√2 √2−1=2k⇒√2−12=kHence, the answer is √2−12.

If $x - 1$ is factor of $(p x) = x^{2} + 2 k x - \sqrt{2} .$ Find the value of $k$