Question

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

3x² + 9x + 4 = 0

Answer 1

Given:

3x² + 9x + 4 = 0

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

a = 3

b = 9

c = 4

D = b² − 4ac

D = 92 − 4(3)(4)

= 81 − 48

= 33

Since D = 33 > 0, the roots are real and unequal

But 33 is not a perfect square, so the roots are irrational

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

`= (-9 +- sqrt33)/(2xx3)`

`= (-9 +- sqrt33)/6`

`= (-9 + sqrt33)/6` or `= (-9 - sqrt33)/6`