WordGPT

Solve 5x² - 11x + 6 = 0

The solutions of 5x² - 11x + 6 = 0 are x = 6/5 or x = 1.

x² +x += 0
5x2−11x+6=0⇒x=65, 15x^2 - 11x + 6 = 0 \Rightarrow x = \frac{6}{5},\ 1
Discriminant D = 1 · x ≈ 1.2, 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 = 5x² - 11x + 6-1.5-1-0.50.511.522.533.55101520253035x = 1.2x = 1vertexy = 5x² - 11x + 6
Graph of y = 5x² - 11x + 6. The curve crosses the x-axis at x = 1.2 and x = 1; the vertex is at (1.1, -0.05).

How to work it out

  1. 1

    Write it in standard form a x² + b x + c = 0 and read off the coefficients: a = 5, b = -11, c = 6.

    5x2−11x+6=05x^2 - 11x + 6 = 0
  2. 2

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

    D=(−11)2−4⋅5⋅6=121−120=1D = (-11)^2 - 4\cdot5\cdot6 = 121 - 120 = 1
  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:

    (5x−6)(x−1)=0\left(5x - 6\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:

    5x−6=0⇒x=65x−1=0⇒x=15x - 6 = 0 \Rightarrow x = \frac{6}{5}\qquad x - 1 = 0 \Rightarrow x = 1
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=11±110x = \frac{-b \pm \sqrt{D}}{2a} = \frac{11 \pm \sqrt{1}}{10}
  7. 7

    Simplify to get the solutions:

    x=65orx=1x = \frac{6}{5}\quad\text{or}\quad x = 1
  8. 8

    Check by putting x = 6/5 back in: a·x² + b·x + c = 5·(36/25) + (-11)·(6/5) + 6 = 0 ✓

LaTeX source of the formulas on this page
\[ 5x^2 - 11x + 6 = 0\ \Rightarrow\ x = \frac{6}{5},\ 1 \]
\[ 5x^2 - 11x + 6 = 0 \]
\[ D = (-11)^2 - 4\cdot5\cdot6 = 121 - 120 = 1 \]
\[ \left(5x - 6\right)\left(x - 1\right) = 0 \]
\[ 5x - 6 = 0 \Rightarrow x = \frac{6}{5}\qquad x - 1 = 0 \Rightarrow x = 1 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{11 \pm \sqrt{1}}{10} \]
\[ x = \frac{6}{5}\quad\text{or}\quad x = 1 \]

The parabola y = 5x² - 11x + 6

xy
-1.944.95
-0.919.95
0.14.95
1.1-0.05
2.14.95
3.119.95
4.144.95

Questions

What are the solutions of 5x² - 11x + 6 = 0?

The solutions of 5x² - 11x + 6 = 0 are x = 6/5 or x = 1.

Does 5x² - 11x + 6 = 0 factor?

Yes: (5x-6)(x-1) = 0.

What is the vertex of y = 5x² - 11x + 6?

(11/10, -1/20). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = 11/5, product = c/a = 6/5.

Similar equations

    Solve 5x² - 11x + 6 = 0: x = 6/5 or x = 1 (steps) | WordGPT