Solve 4x² = 0

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

x² +x += 0

4x^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.

4x^2 = 0\ \Rightarrow\ x = 0

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Graph of y = 4x². The curve crosses the x-axis at x = 0; the vertex is at (0, 0).

How to work it out

1
Write it in standard form a x² + b x + c = 0 and read off the coefficients: a = 4, b = 0, c = 0.
$4x^2 = 0$
2
Work out the discriminant D = b² − 4ac. Its sign tells you how many real solutions there are.
$D = 0^2 - 4\cdot4\cdot0 = 0 + 0 = 0$
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:
$4\left(x\right)\left(x\right) = 0$
5
A product is zero when one of its factors is zero, so set each factor equal to 0 and solve:
$x = 0 \Rightarrow x = 0$
6
Method 2, The quadratic formula works for every quadratic:
$x = \frac{-b \pm \sqrt{D}}{2a} = \frac{0 \pm \sqrt{0}}{8}$
7
Simplify to get the solution:
$x = 0$
8
Check by putting x = 0 back in: a·x² + b·x + c = 4·(0) + 0·(0) + 0 = 0 ✓

LaTeX source of the formulas on this page

\[ 4x^2 = 0\ \Rightarrow\ x = 0 \]
\[ 4x^2 = 0 \]
\[ D = 0^2 - 4\cdot4\cdot0 = 0 + 0 = 0 \]
\[ 4\left(x\right)\left(x\right) = 0 \]
\[ x = 0 \Rightarrow x = 0 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{0 \pm \sqrt{0}}{8} \]
\[ x = 0 \]

The parabola y = 4x²

x	y
-3	36
-2	16
-1	4
0	0
1	4
2	16
3	36

Questions

What are the solutions of 4x² = 0?

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

Does 4x² = 0 factor?

Yes: 4(x)(x) = 0.

What is the vertex of y = 4x²?

(0, 0). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = 0, product = c/a = 0.

Solve 4x² = 0

How to work it out

The parabola y = 4x²

Questions

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