The discriminant
The question
x² + 35x + 44 = 0
How many real solutions?
x² + 35x + 44 = 0
x² + 35x + 44 = 0
a = 1b = 35c = 44
b² − 4ac = 35² − 4(1)(44)
= 1049 > 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 x² + 35x + 44 = 0: a = 1, b = 35, c = 44.
- Work it out: 35² is 1225, and 4 × 1 × 44 is 176. That leaves 1225 − 176 = 1049.
- 1049 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 x² + 35x + 44 = 0: a = 1, b = 35, c = 44.
- 03
Work it out: 35² is 1225, and 4 × 1 × 44 is 176. That leaves 1225 − 176 = 1049.
- 04
1049 is above zero, and a positive number has two square roots — one either way from the ±. So there are TWO real solutions.