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Solve -2x² - 4x - 2 = 0

The solution of -2x² - 4x - 2 = 0 is x = -1 (a repeated root).

x² +x += 0
−2x2−4x−2=0⇒x=−1-2x^2 - 4x - 2 = 0 \Rightarrow x = -1
Discriminant D = 0 · x ≈ -1

Change a, b or c (whole numbers, a not 0) and the exact solutions follow.

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Graph of y = -2x² - 4x - 2-3.5-3-2.5-2-1.5-1-0.50.511.5-12-10-8-6-4-2x = -1vertexy = -2x² - 4x - 2
Graph of y = -2x² - 4x - 2. The curve crosses the x-axis at x = -1; the vertex is at (-1, 0).

How to work it out

  1. 1

    Write it in standard form a x² + b x + c = 0 and read off the coefficients: a = -2, b = -4, c = -2.

    −2x2−4x−2=0-2x^2 - 4x - 2 = 0
  2. 2

    Work out the discriminant D = b² − 4ac. Its sign tells you how many real solutions there are.

    D=(−4)2−4⋅(−2)⋅(−2)=16−16=0D = (-4)^2 - 4\cdot(-2)\cdot(-2) = 16 - 16 = 0
  3. 3

    D is zero, so there is exactly one solution (a repeated root).

  4. 4

    Method 1, factoring. The roots are rational, so the left side factors:

    −2(x+1)(x+1)=0-2\left(x + 1\right)\left(x + 1\right) = 0
  5. 5

    A product is zero when one of its factors is zero, so set each factor equal to 0 and solve:

    x+1=0⇒x=−1x + 1 = 0 \Rightarrow x = -1
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=4±0−4x = \frac{-b \pm \sqrt{D}}{2a} = \frac{4 \pm \sqrt{0}}{-4}
  7. 7

    Simplify to get the solution:

    x=−1x = -1
  8. 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

xy
-4-18
-3-8
-2-2
-10
0-2
1-8
2-18

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.

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