Chapter 4.2, Problem 2CYU

To determine

To solve: the solution of the given equation by using the related graph.

Answer to Problem 2CYU

  $-2\text{ and }5$ .

Explanation of Solution

Given:

The given equation is $x^2-3x-10=0$ .

The related graph is:

  

Calculation:

The given equation is $x^2-3x-10=0$ .

Now, to find the solution of the given equation.

Now, to find the solution of quadratic equation, the roots of the equation is known. This could be solved by finding the zeros of the related quadratic function. The zeros of the function are the x -intercept of its graph.

Looking at the graph, the parabola crosses the x -axis, therefore, $x=-2,x=5$ .

Zeroth of the quadratic equation:

  $\begin{array}{l}f\left(x\right)=x^2-3x-10\left\{\text{given function}\right\}\\ f\left(-2\right)={\left(-2\right)}^2-3\left(-2\right)-10\{\text{substitute }x=-2\}\\ f\left(-2\right)=4-\left(6\right)-10\{\text{evaluate the power} }\\ f\left(-2\right)=4+6-10\left\{\text{multiply}\right\}\\ f\left(-2\right)=0=0\left\{performtheoperation\right\}\end{array}$

  $\begin{array}{l}f\left(x\right)=x^2-3x-10\left\{\text{given function}\right\}\\ f\left(-5\right)={\left(-5\right)}^2-3\left(-5\right)-10\{\text{substitute }x=-5\}\\ f\left(-5\right)=25-\left(15\right)-10\{\text{evaluate the power} }\\ f\left(-5\right)=25-25\left\{\text{multiply}\right\}\\ f\left(-5\right)=0\left\{performtheoperation\right\}\end{array}$

Thus, the zeros of the function are $-2\text{ and }5$ .

Hence, the solution of the given equation is $-2\text{ and }5$ .