WordGPT

Solve 5x² - 8x + 3 = 0

The solutions of 5x² - 8x + 3 = 0 are x = 1 or x = 3/5.

x² +x += 0
5x2−8x+3=0⇒x=1, 355x^2 - 8x + 3 = 0 \Rightarrow x = 1,\ \frac{3}{5}
Discriminant D = 4 · x ≈ 1, 0.6

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 - 8x + 3-1123-55101520253035x = 1x = 0.6vertexy = 5x² - 8x + 3
Graph of y = 5x² - 8x + 3. The curve crosses the x-axis at x = 1 and x = 0.6; the vertex is at (0.8, -0.2).

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 = -8, c = 3.

    5x2−8x+3=05x^2 - 8x + 3 = 0
  2. 2

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

    D=(−8)2−4⋅5⋅3=64−60=4D = (-8)^2 - 4\cdot5\cdot3 = 64 - 60 = 4
  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−1)(5x−3)=0\left(x - 1\right)\left(5x - 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−1=0⇒x=15x−3=0⇒x=35x - 1 = 0 \Rightarrow x = 1\qquad 5x - 3 = 0 \Rightarrow x = \frac{3}{5}
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=8±410x = \frac{-b \pm \sqrt{D}}{2a} = \frac{8 \pm \sqrt{4}}{10}
  7. 7

    Simplify to get the solutions:

    x=1orx=35x = 1\quad\text{or}\quad x = \frac{3}{5}
  8. 8

    Check by putting x = 1 back in: a·x² + b·x + c = 5·(1) + (-8)·(1) + 3 = 0 ✓

LaTeX source of the formulas on this page
\[ 5x^2 - 8x + 3 = 0\ \Rightarrow\ x = 1,\ \frac{3}{5} \]
\[ 5x^2 - 8x + 3 = 0 \]
\[ D = (-8)^2 - 4\cdot5\cdot3 = 64 - 60 = 4 \]
\[ \left(x - 1\right)\left(5x - 3\right) = 0 \]
\[ x - 1 = 0 \Rightarrow x = 1\qquad 5x - 3 = 0 \Rightarrow x = \frac{3}{5} \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{8 \pm \sqrt{4}}{10} \]
\[ x = 1\quad\text{or}\quad x = \frac{3}{5} \]

The parabola y = 5x² - 8x + 3

xy
-2.244.8
-1.219.8
-0.24.8
0.8-0.2
1.84.8
2.819.8
3.844.8

Questions

What are the solutions of 5x² - 8x + 3 = 0?

The solutions of 5x² - 8x + 3 = 0 are x = 1 or x = 3/5.

Does 5x² - 8x + 3 = 0 factor?

Yes: (x-1)(5x-3) = 0.

What is the vertex of y = 5x² - 8x + 3?

(4/5, -1/5). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = 8/5, product = c/a = 3/5.

Similar equations

    Solve 5x² - 8x + 3 = 0: x = 1 or x = 3/5 (steps) | WordGPT