WordGPT

Solve 4x² + 3x = 0

The solutions of 4x² + 3x = 0 are x = 0 or x = -3/4.

x² +x += 0
4x2+3x=0⇒x=0, −344x^2 + 3x = 0 \Rightarrow x = 0,\ -\frac{3}{4}
Discriminant D = 9 · x ≈ 0, -0.75

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

Explain it step by step in chatMake a short video of it
Graph of y = 4x² + 3x-3-2-1125101520253035x = 0x = -0.75vertexy = 4x² + 3x
Graph of y = 4x² + 3x. The curve crosses the x-axis at x = 0 and x = -0.75; the vertex is at (-0.375, -0.5625).

How to work it out

  1. 1

    Write it in standard form a x² + b x + c = 0 and read off the coefficients: a = 4, b = 3, c = 0.

    4x2+3x=04x^2 + 3x = 0
  2. 2

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

    D=32−4⋅4⋅0=9+0=9D = 3^2 - 4\cdot4\cdot0 = 9 + 0 = 9
  3. 3

    D is positive, so there are two different real solutions.

  4. 4

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

    (x)(4x+3)=0\left(x\right)\left(4x + 3\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=04x+3=0⇒x=−34x = 0 \Rightarrow x = 0\qquad 4x + 3 = 0 \Rightarrow x = -\frac{3}{4}
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=−3±98x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-3 \pm \sqrt{9}}{8}
  7. 7

    Simplify to get the solutions:

    x=0orx=−34x = 0\quad\text{or}\quad x = -\frac{3}{4}
  8. 8

    Check by putting x = 0 back in: a·x² + b·x + c = 4·(0) + 3·(0) + 0 = 0 ✓

LaTeX source of the formulas on this page
\[ 4x^2 + 3x = 0\ \Rightarrow\ x = 0,\ -\frac{3}{4} \]
\[ 4x^2 + 3x = 0 \]
\[ D = 3^2 - 4\cdot4\cdot0 = 9 + 0 = 9 \]
\[ \left(x\right)\left(4x + 3\right) = 0 \]
\[ x = 0 \Rightarrow x = 0\qquad 4x + 3 = 0 \Rightarrow x = -\frac{3}{4} \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-3 \pm \sqrt{9}}{8} \]
\[ x = 0\quad\text{or}\quad x = -\frac{3}{4} \]

The parabola y = 4x² + 3x

xy
-3.37535.4375
-2.37515.4375
-1.3753.4375
-0.375-0.5625
0.6253.4375
1.62515.4375
2.62535.4375

Questions

What are the solutions of 4x² + 3x = 0?

The solutions of 4x² + 3x = 0 are x = 0 or x = -3/4.

Does 4x² + 3x = 0 factor?

Yes: (x)(4x+3) = 0.

What is the vertex of y = 4x² + 3x?

(-3/8, -9/16). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = -3/4, product = c/a = 0.

Similar equations

    Solve 4x² + 3x = 0: x = 0 or x = -3/4 (steps) | WordGPT