Question

Determine whether the following equation has real roots or not. If yes, find them:

7x² + 8x + 2 = 0

Answer 1

Given:

7x² + 8x + 2 = 0

This is in the standard form ax² + bx + c = 0, where:

a = 7

b = 8

c = 2

D = b² − 4ac

= 8² − 4(7) (2) 

= 64 − 56

= 8

Since D = 8 > 0, the equation has two real and unequal roots.

Since D is not a perfect square, the roots are irrational.

`x = (-b +- sqrtD)/(2a)`

`= (-8+-sqrt8)/2.7`

`= (-8+-2sqrt2)/14`

`x = (-4+-sqrt2)/7`

`x = (-4+sqrt2)/7` or `x = (-4-sqrt2)/7`