Q. 534 - Intermediate Algebra

Question

Use the discriminant to determine the number and type of solutions of each quadratic equation.

$6p^2-13p+7=0$

Step-by-Step Solution

Answer

There are $2$ real solutions.

Step 1. Given information.

We have:

$6p^2-13p+7=0$

Step 2. Find the number of solution using discriminant.

Determine the number of solutions:

$6p^2-13p+7=0$

Comparing the equation with standard form of quadratic equation $a{x}^2+bx+c=0$, it follows:

$a=6,b=13,c=7$

Substitute the coefficients into the expression:

$$\begin{gathered} D=b^2-4ac \\ D={\left(-13\right)}^2-4·6·7 \\ D=169-168 \\ D=1 \end{gathered}$$

Therefore, the quadratic equation has $2$ real solutions because $D>0.$