Question

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

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

Short answer

As a result, the equation has two distinct solutions.

Step-by-step solution

Given information.

The given equation is.

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

Determine the number of solutions to each quadratic equation using the discriminant.

First, write the equation $a{x}^2+bx+c=0$a in standard form, as shown below.

Determine the a, b, and c values.

In comparison to the standard form, the values are a = 6,b = -13, and c= 7.

Calculate the discriminant $b^2-4ac$now.

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

Because the discriminant is positive, the equation has two real solutions.

As a result, the equation has two distinct solutions.