Question

Find the value of k if x-1 is a factor of P(X) = kx²-√5+k​

Answer 1

EXPLANATION.

x - 1 is the factor of.

⇒ p(x) = kx² - √5x + k.

As we know that,

⇒ (x - 1) = 0.

⇒ x = 1.

Put the value of x = 1 in the equation, we get.

⇒ kx² - √5x + k = 0.

⇒ k(1)² - √5(1) + k = 0.

⇒ k + k - √5 = 0.

⇒ 2k - √5 = 0.

⇒ 2k = √5.

⇒ k = √5/2.

                                                                                                                           

MORE INFORMATION.

Conjugate roots.

(1) = If D < 0.

One roots = α + iβ.

Other roots = α - iβ.

(2) = If D > 0.

One roots = α + √β.

Other roots = α - √β.

Answer 2

k = (√5)/2

Step-by-step explanation:

x - 1 = 0 , x = 1

then ,

p(1) = k(1)² - √5(1) + k = 0

k - √5 + k = 0

2k = √5

k = (√5)/2