WordGPT

Solve 4x² - 12x + 8 = 0

The solutions of 4x² - 12x + 8 = 0 are x = 2 or x = 1.

x² +x += 0
4x2−12x+8=0⇒x=2, 14x^2 - 12x + 8 = 0 \Rightarrow x = 2,\ 1
Discriminant D = 16 · x ≈ 2, 1

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 - 12x + 8-11234-55101520253035x = 2x = 1vertexy = 4x² - 12x + 8
Graph of y = 4x² - 12x + 8. The curve crosses the x-axis at x = 2 and x = 1; the vertex is at (1.5, -1).

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 = -12, c = 8.

    4x2−12x+8=04x^2 - 12x + 8 = 0
  2. 2

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

    D=(−12)2−4⋅4⋅8=144−128=16D = (-12)^2 - 4\cdot4\cdot8 = 144 - 128 = 16
  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:

    4(x−2)(x−1)=04\left(x - 2\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−2=0⇒x=2x−1=0⇒x=1x - 2 = 0 \Rightarrow x = 2\qquad x - 1 = 0 \Rightarrow x = 1
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=12±168x = \frac{-b \pm \sqrt{D}}{2a} = \frac{12 \pm \sqrt{16}}{8}
  7. 7

    Simplify to get the solutions:

    x=2orx=1x = 2\quad\text{or}\quad x = 1
  8. 8

    Check by putting x = 2 back in: a·x² + b·x + c = 4·(4) + (-12)·(2) + 8 = 0 ✓

LaTeX source of the formulas on this page
\[ 4x^2 - 12x + 8 = 0\ \Rightarrow\ x = 2,\ 1 \]
\[ 4x^2 - 12x + 8 = 0 \]
\[ D = (-12)^2 - 4\cdot4\cdot8 = 144 - 128 = 16 \]
\[ 4\left(x - 2\right)\left(x - 1\right) = 0 \]
\[ x - 2 = 0 \Rightarrow x = 2\qquad x - 1 = 0 \Rightarrow x = 1 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{12 \pm \sqrt{16}}{8} \]
\[ x = 2\quad\text{or}\quad x = 1 \]

The parabola y = 4x² - 12x + 8

xy
-1.535
-0.515
0.53
1.5-1
2.53
3.515
4.535

Questions

What are the solutions of 4x² - 12x + 8 = 0?

The solutions of 4x² - 12x + 8 = 0 are x = 2 or x = 1.

Does 4x² - 12x + 8 = 0 factor?

Yes: 4(x-2)(x-1) = 0.

What is the vertex of y = 4x² - 12x + 8?

(3/2, -1). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = 3, product = c/a = 2.

Similar equations

    Solve 4x² - 12x + 8 = 0: x = 2 or x = 1 (steps) | WordGPT