Q9. - Algebra 1

Question

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

$x^2+5x+6=0$

Step-by-Step Solution

Answer

The roots of the equation $x^2+5x+6=0$ are $\mathit{x}\mathbf{=}\mathbf{-}\mathbf{3}$ and $\mathit{x}\mathbf{=}\mathbf{-}\mathbf{2}$.

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, $f\left(x\right)=a{x}^2+bx+c$, where, $a\ne 0$ is called the standard form of the quadratic function.

Step 2. Rewrite the equation x 2 + 5 x + 6 = 0 in the form f x = a x 2 + b x + c .

Write the equation $x^2+5x+6=0$ in standard form.

This equation is already in standard form.

Write the equation $x^2+5x+6=0$ in the form $f\left(x\right)=a{x}^2+bx+c$.

$f\left(x\right)=x^2+5x+6$

Step 3. Plot the graph of the function f x = x 2 + 5 x + 6 .

The graph of the function $f\left(x\right)=x^2+5x+6$ is shown below.

Step 4. Solve the equation x 2 + 5 x + 6 = 0 from the graph of the function f x = x 2 + 5 x + 6 .

Observe the graph of the function $f\left(x\right)=x^2+5x+6$.

The graph intersects the $x$- axis at the points $x=-3$ and $x=-2$.  

Therefore the roots of the equation $x^2+5x+6=0$ are $x=-3$ and $x=-2$.