Question

Use the discriminant to describe the number and type of roots for the equation.



12⁢𝑥2+9⁢𝑥+1=0



number of roots:
2

type of root(s): irrational root(s)

Answer 1

Compute discriminant: D = b^2 − 4ac = 9^2 − 4(12)(1) = 81 − 48 = 33.

Since D > 0 there are 2 distinct real roots. Because 33 is not a perfect square, the roots are irrational.

Exact roots: x = (−9 ± √33) / 24 (equivalently x = −3/8 ± √33/24).