Question

(1)-1 (1) Find the value of k for which x= 1 is a root of the equation xsquare+Kx+3=0, Also find the other root
​

Answer 1

Required Answer :

• The value of k = - 4
• The other root of the equation = 3

Given :

• x = 1 is a root of the equation x² + kx + 3 = 0

To find :

• The value of k
• The value of the other root of the equation

Solution :

Finding the value of k :

⇒ x² + kx + 3 = 0

Substitute the value of x in the equation :

⇒ (1)² + k(1) + 3 = 0

⇒ 1 + k + 3 = 0

⇒ k + 4 = 0

⇒ k = - 4

The value of k = - 4

Finding the other root :

Substitute the value of k in the equation :

⇒ x² + kx + 3 = 0

⇒ x² + (-4)x + 3 = 0

⇒ x² - 4x + 3 = 0

⇒ Product of the quadratic equation = 3x²

⇒ x² - 3x - 1x + 3 = 0

⇒ x(x - 3) - 1(x - 3) = 0

⇒ (x - 1)(x - 3) = 0

⇒ (x - 1) = 0 or (x - 3) = 0

⇒ x - 1 = 0 or x - 3 = 0

⇒ x = 1 or x = 3

Therefore, the other root of the equation = 3