Question

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



3⁢𝑥^2−16⁢𝑥+16=0

Answer 1

For 3x^2 − 16x + 16 = 0, a = 3, b = −16, c = 16.

Discriminant Δ = b^2 − 4ac = (−16)^2 − 4·3·16 = 256 − 192 = 64.

Since Δ > 0, there are two distinct real roots. Because Δ is a perfect square, the roots are rational:

x = [−b ± √Δ]/(2a) = [16 ± 8]/6, so x = 4 and x = 4/3.