WordGPT

Solve 3x² + 9x + 6 = 0

The solutions of 3x² + 9x + 6 = 0 are x = -1 or x = -2.

x² +x += 0
3x2+9x+6=0⇒x=−1, −23x^2 + 9x + 6 = 0 \Rightarrow x = -1,\ -2
Discriminant D = 9 · x ≈ -1, -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 = 3x² + 9x + 6-4-3-2-11510152025x = -1x = -2vertexy = 3x² + 9x + 6
Graph of y = 3x² + 9x + 6. The curve crosses the x-axis at x = -1 and x = -2; the vertex is at (-1.5, -0.75).

How to work it out

  1. 1

    Write it in standard form a x² + b x + c = 0 and read off the coefficients: a = 3, b = 9, c = 6.

    3x2+9x+6=03x^2 + 9x + 6 = 0
  2. 2

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

    D=92−4⋅3⋅6=81−72=9D = 9^2 - 4\cdot3\cdot6 = 81 - 72 = 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:

    3(x+1)(x+2)=03\left(x + 1\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:

    x+1=0⇒x=−1x+2=0⇒x=−2x + 1 = 0 \Rightarrow x = -1\qquad x + 2 = 0 \Rightarrow x = -2
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=−9±96x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-9 \pm \sqrt{9}}{6}
  7. 7

    Simplify to get the solutions:

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

    Check by putting x = -1 back in: a·x² + b·x + c = 3·(1) + 9·(-1) + 6 = 0 ✓

LaTeX source of the formulas on this page
\[ 3x^2 + 9x + 6 = 0\ \Rightarrow\ x = -1,\ -2 \]
\[ 3x^2 + 9x + 6 = 0 \]
\[ D = 9^2 - 4\cdot3\cdot6 = 81 - 72 = 9 \]
\[ 3\left(x + 1\right)\left(x + 2\right) = 0 \]
\[ x + 1 = 0 \Rightarrow x = -1\qquad x + 2 = 0 \Rightarrow x = -2 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-9 \pm \sqrt{9}}{6} \]
\[ x = -1\quad\text{or}\quad x = -2 \]

The parabola y = 3x² + 9x + 6

xy
-4.526.25
-3.511.25
-2.52.25
-1.5-0.75
-0.52.25
0.511.25
1.526.25

Questions

What are the solutions of 3x² + 9x + 6 = 0?

The solutions of 3x² + 9x + 6 = 0 are x = -1 or x = -2.

Does 3x² + 9x + 6 = 0 factor?

Yes: 3(x+1)(x+2) = 0.

What is the vertex of y = 3x² + 9x + 6?

(-3/2, -3/4). 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 3x² + 9x + 6 = 0: x = -1 or x = -2 (steps) | WordGPT