Discriminant with a leading coefficient
The question
8x² − 16x − 90 = 0
How many real solutions?
8x² − 16x − 90 = 0
8x² − 16x − 90 = 0
a = 8b = −16c = −90
b² − 4ac = (−16)² − 4(8)(−90)
= 3136 > 0→two
- You do not have to solve it. The discriminant, b² − 4ac — the part under the square root in the quadratic formula — tells you how many real solutions there are.
- Read off a, b and c from 8x² − 16x − 90 = 0: a = 8, b = −16, c = −90.
- Work it out: (−16)² is 256, and 4 × 8 × −90 is −2880. That leaves 256 − −2880 = 3136.
- 3136 is above zero, and a positive number has two square roots — one either way from the ±. So there are TWO real solutions.
How it works.
- 01
You do not have to solve it. The discriminant, b² − 4ac — the part under the square root in the quadratic formula — tells you how many real solutions there are.
- 02
Read off a, b and c from 8x² − 16x − 90 = 0: a = 8, b = −16, c = −90.
- 03
Work it out: (−16)² is 256, and 4 × 8 × −90 is −2880. That leaves 256 − −2880 = 3136.
- 04
3136 is above zero, and a positive number has two square roots — one either way from the ±. So there are TWO real solutions.