Question

please solve the above questions
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Answer 1

Question :

Find the value of k, if (x - 1) is a factor of :-

1. p(x) = x² + x + k
2. p(x) = kx² - √3 x + 1

To find :

• The value of k

Solution :

Here, in his question we are given two equations and their factor and we need to calculate the value of k. So, for that substitute the value of 'x' in the equation and keep the equation equal to zero.

(x - 1) is a factor of p(x) = x² + x + k

⇒ (x - 1) = 0

⇒ x = 1

⇒ p(x) = x² + x + k = 0

Substituting the value of x = 1 in the equation :

⇒ p(1) = (1)² + 1 + k = 0

⇒ 1 + 1 + k = 0

⇒ 2 + k = 0

⇒ k = - 2

Therefore, the value of k = - 2

(x - 1) is a factor of p(x) = kx² - √3 x + 1

⇒ (x - 1) = 0

⇒ x = 1

⇒ p(x) = kx² - √3 x + 1 = 0

Substituting the value of x = 1 in the equation :

⇒p(1) = k(1)² - √3 (1) + 1 = 0

⇒ k(1) - √3 + 1 = 0

⇒ k - √3 + 1 = 0

⇒ k = √3 - 1

Therefore, the value of k = √3 - 1