Question

If one root of the equation 5x² + kx − 2 = 0 is 1, find the value of k and also find other root.

Answer 1

Given:

5x² + kx − 2 = 0

x = 1

5(1)² + k(1) − 2 = 0

⇒ 5 + k − 2 = 0

⇒ k + 3 = 0

⇒ k = −3

5x2 − 3x − 2 = 0

`x = (-(-3) +- sqrt((-3)^2-4(5)(-2)))/(2(5))`

`=(3+- sqrt(9+40))/10`

`= (3+-sqrt49)/10`

`= (3+-7)/10`

`x = (3+7)/10 = 10/10 = 1`

`x = (3-7)/10 = (-4)/10 = -2/5`

Value of k = −3

Other root = `-2/5`