Question

find the value of k, if x-2 is a factor of the polynomial p(x)=kx²-√2x+1

Answer 1

Hey!!!!!

Good Afternoon

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We have

=> p(x) = kx² - √2x + 1

since x - 2 is a factor

=> x - 2 = 0

=> x = 2

Thus p(2) = 0

=> k(2)² - √2(2) + 1 = 0

=> 4k - 2√2 + 1 = 0

=> 4k = 2√2 - 1

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

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Hope this helps ✌️

Answer 2

Hey!

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(x - 2) is the factor of p(x) , that means,

x -2 = 0
x = 2

Keeping value of x -:

p (x) = kx²-√2x+1 = p

p (2) = 4k - √2 × 2 + 1 = 0

4k - 2√2 + 1 = 0

k = 2√2 - 1/4

We got the value of k.

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Hope it helps...!!!