Solve -2x² + 4x - 2 = 0
The solution of -2x² + 4x - 2 = 0 is x = 1 (a repeated root).
Change a, b or c (whole numbers, a not 0) and the exact solutions follow.
How to work it out
- 1
Write it in standard form a x² + b x + c = 0 and read off the coefficients: a = -2, b = 4, c = -2.
- 2
Work out the discriminant D = b² − 4ac. Its sign tells you how many real solutions there are.
- 3
D is zero, so there is exactly one solution (a repeated root).
- 4
Method 1, factoring. The roots are rational, so the left side factors:
- 5
A product is zero when one of its factors is zero, so set each factor equal to 0 and solve:
- 6
Method 2, The quadratic formula works for every quadratic:
- 7
Simplify to get the solution:
- 8
Check by putting x = 1 back in: a·x² + b·x + c = -2·(1) + 4·(1) + (-2) = 0 ✓
LaTeX source of the formulas on this page
\[ -2x^2 + 4x - 2 = 0\ \Rightarrow\ x = 1 \]
\[ -2x^2 + 4x - 2 = 0 \]
\[ D = 4^2 - 4\cdot(-2)\cdot(-2) = 16 - 16 = 0 \]
\[ -2\left(x - 1\right)\left(x - 1\right) = 0 \]
\[ x - 1 = 0 \Rightarrow x = 1 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-4 \pm \sqrt{0}}{-4} \]
\[ x = 1 \]The parabola y = -2x² + 4x - 2
| x | y |
|---|---|
| -2 | -18 |
| -1 | -8 |
| 0 | -2 |
| 1 | 0 |
| 2 | -2 |
| 3 | -8 |
| 4 | -18 |
Questions
What are the solutions of -2x² + 4x - 2 = 0?
The solution of -2x² + 4x - 2 = 0 is x = 1 (a repeated root).
Does -2x² + 4x - 2 = 0 factor?
Yes: -2(x-1)(x-1) = 0.
What is the vertex of y = -2x² + 4x - 2?
(1, 0). The parabola opens downwards, so this is the maximum.
What are the sum and product of the roots?
Sum = −b/a = 2, product = c/a = 1.