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Solve -x² = 0

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

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

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

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Graph of y = -x²-2.5-2-1.5-1-0.50.511.522.5-6-5-4-3-2-1x = 0vertexy = -x²
Graph of y = -x². The curve crosses the x-axis at x = 0; the vertex is at (0, 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 = -1, b = 0, c = 0.

    −x2=0-x^2 = 0
  2. 2

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

    D=02−4⋅(−1)⋅0=0+0=0D = 0^2 - 4\cdot(-1)\cdot0 = 0 + 0 = 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:

    −(x)(x)=0-\left(x\right)\left(x\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=0⇒x=0x = 0 \Rightarrow x = 0
  6. 6

    Method 2, The quadratic formula works for every quadratic:

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

    Simplify to get the solution:

    x=0x = 0
  8. 8

    Check by putting x = 0 back in: a·x² + b·x + c = -1·(0) + 0·(0) + 0 = 0 ✓

LaTeX source of the formulas on this page
\[ -x^2 = 0\ \Rightarrow\ x = 0 \]
\[ -x^2 = 0 \]
\[ D = 0^2 - 4\cdot(-1)\cdot0 = 0 + 0 = 0 \]
\[ -\left(x\right)\left(x\right) = 0 \]
\[ x = 0 \Rightarrow x = 0 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{0 \pm \sqrt{0}}{-2} \]
\[ x = 0 \]

The parabola y = -x²

xy
-3-9
-2-4
-1-1
00
1-1
2-4
3-9

Questions

What are the solutions of -x² = 0?

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

Does -x² = 0 factor?

Yes: -1(x)(x) = 0.

What is the vertex of y = -x²?

(0, 0). The parabola opens downwards, so this is the maximum.

What are the sum and product of the roots?

Sum = −b/a = 0, product = c/a = 0.

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