please solve the above questions
fastt
Attachments:
Answers
Answered by
44
Question :
Find the value of k, if (x - 1) is a factor of :-
- p(x) = x² + x + k
- 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
Similar questions
History,
3 hours ago
Computer Science,
3 hours ago
Math,
3 hours ago
Math,
5 hours ago
Business Studies,
5 hours ago
Math,
7 months ago
Environmental Sciences,
7 months ago