WordGPT

Solve 4x² + 2x - 12 = 0

The solutions of 4x² + 2x - 12 = 0 are x = 3/2 or x = -2.

x² +x += 0
4x2+2x−12=0⇒x=32, −24x^2 + 2x - 12 = 0 \Rightarrow x = \frac{3}{2},\ -2
Discriminant D = 196 · x ≈ 1.5, -2

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 + 2x - 12-4-3-2-11234-20-10102030405060x = 1.5x = -2vertexy = 4x² + 2x - 12
Graph of y = 4x² + 2x - 12. The curve crosses the x-axis at x = 1.5 and x = -2; the vertex is at (-0.25, -12.25).

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 = 2, c = -12.

    4x2+2x−12=04x^2 + 2x - 12 = 0
  2. 2

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

    D=22−4⋅4⋅(−12)=4+192=196D = 2^2 - 4\cdot4\cdot(-12) = 4 + 192 = 196
  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:

    2(2x−3)(x+2)=02\left(2x - 3\right)\left(x + 2\right) = 0
  5. 5

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

    2x−3=0⇒x=32x+2=0⇒x=−22x - 3 = 0 \Rightarrow x = \frac{3}{2}\qquad x + 2 = 0 \Rightarrow x = -2
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=−2±1968x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-2 \pm \sqrt{196}}{8}
  7. 7

    Simplify to get the solutions:

    x=32orx=−2x = \frac{3}{2}\quad\text{or}\quad x = -2
  8. 8

    Check by putting x = 3/2 back in: a·x² + b·x + c = 4·(9/4) + 2·(3/2) + (-12) = 0 ✓

LaTeX source of the formulas on this page
\[ 4x^2 + 2x - 12 = 0\ \Rightarrow\ x = \frac{3}{2},\ -2 \]
\[ 4x^2 + 2x - 12 = 0 \]
\[ D = 2^2 - 4\cdot4\cdot(-12) = 4 + 192 = 196 \]
\[ 2\left(2x - 3\right)\left(x + 2\right) = 0 \]
\[ 2x - 3 = 0 \Rightarrow x = \frac{3}{2}\qquad x + 2 = 0 \Rightarrow x = -2 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-2 \pm \sqrt{196}}{8} \]
\[ x = \frac{3}{2}\quad\text{or}\quad x = -2 \]

The parabola y = 4x² + 2x - 12

xy
-3.2523.75
-2.253.75
-1.25-8.25
-0.25-12.25
0.75-8.25
1.753.75
2.7523.75

Questions

What are the solutions of 4x² + 2x - 12 = 0?

The solutions of 4x² + 2x - 12 = 0 are x = 3/2 or x = -2.

Does 4x² + 2x - 12 = 0 factor?

Yes: 2(2x-3)(x+2) = 0.

What is the vertex of y = 4x² + 2x - 12?

(-1/4, -49/4). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = -1/2, product = c/a = -3.

Similar equations

    Solve 4x² + 2x - 12 = 0: x = 3/2 or x = -2 (steps) | WordGPT