If x-2 is a factor of kx2-2x-1- then find the value of k

We have, #10; #10; x 2 is a factor of kx^2 √(2)x+1 #10; #10;Then, #10; #10; x 2=0 #10; #10; x=2 #10; #10;Put in the giv ...

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Standard X

Physics

Resistivity

If x-2 is a...

Question

If $x - 2$ is a factor of $k x^{2} - \sqrt{2} x + 1$ , then find the value of $k$

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Solution

We have,

$x - 2$ is a factor of $k x^{2} - \sqrt{2} x + 1$

Then,

$x - 2 = 0$

$x = 2$

Put in the given equation

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

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

$4 k = 2 \sqrt{2} - 1$

$k = \frac{2 \sqrt{2} - 1}{4}$

Hence, this is the answer.

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Similar questions

Q. Find the value of

k

, if

x - 1

is a factor of

p (x) = k x^{2} - \sqrt{2} x + 1

Q. Find the value of

k

, if

2 x - 3

is a factor of

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Q. Find the value of

k

, if

x - 1

is a factor of

p (x)

in each of the following cases:
(i)

p (x) = x^{2} + x + k

(ii)

p (x) = 2 x^{2} + k x + \sqrt{2}

(iii)

p (x) = k x^{2} - \sqrt{2} x + 1

(iv)

p (x) = k x^{2} - 3 x + k

find the value of k if (x-1) is a factor of the polynomial kx²-3x+k

Find the value of k, if x - 1 is a factor p(x) in each of the following cases:
(i) $p (x) = x^{2} + x + k$
(ii) $p (x) = 2 x^{2} + k x + \sqrt{2}$
(iii) $p (x) = k x^{2} - \sqrt{2} x + 1$
(iv) $p (x) = k x^{2} - 3 x + k$

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If x−2 is a factor of kx2−√2x+1, then find the value of k

We have, x−2 is a factor of kx2−√2x+1 Then, x−2=0 x=2 Put in the given equation k(2)2−√2(2)+1=0 4k−2√2+1=0 4k=2√2−1 k=2√2−14 Hence, this is the answer.

If $x - 2$ is a factor of $k x^{2} - \sqrt{2} x + 1$ , then find the value of $k$

We have,

$x - 2$ is a factor of $k x^{2} - \sqrt{2} x + 1$

Then,

$x - 2 = 0$

$x = 2$

Put in the given equation

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

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

$4 k = 2 \sqrt{2} - 1$

$k = \frac{2 \sqrt{2} - 1}{4}$

Hence, this is the answer.