Question

find the value of k if x minus 1 is a factor of P of X equal to K x square minus root 2 X + 1​

Answer 1

Step-by-step explanation:

x-1 = 0

x = 1

P(x) = kx^2 - √2x +1

P(1) = k - √2 +1

k = √2-1

Answer 2

Given,

x minus 1 is a factor of P of X equal to K x square minus root 2 X + 1.

To find,

The value of k.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

If (x+a) and (x+b) are two factors of a quadratic equation p(x), then (-a) and (-b) are two roots of the given quadratic equation and p(-a) = p(-b) = 0. {Statement-1}

According to the question;

x minus 1 is a factor of P of X equal to K x square minus root 2 X + 1

=> (x-1) is a factor of P(x) = kx^2 - √2x + 1

=> P(1) = 0

{according to statement-1}

=> k(1)^2 - √2(1) + 1 = 0

=> k - √2 + 1 = 0

=> k = (√2-1)

Hence, the value of k is equal to (√2-1).