Question

In the following exercises, solve by using the Quadratic Formula. $2p^2-7p+3=0$

Short answer

The solution of the quadratic equation is$p=3$and$p=\frac{1}{2}$

Step-by-step solution

Given information

We are given a quadratic equation$2p^2-7p+3=0$

identify the values of a,b,c

On comparing with the standard equation we get$a=2,b=-7,c=3$

Write quadratic formula and substitute the values in it

The quadratic formula can be given as

$p=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

On substituting the values we get

$p=\frac{7\pm \sqrt{49-4\left(2\right)\left(3\right)}}{2\left(2\right)}$

Simplify

On simplifying we get

$$\begin{gathered} p=\frac{7\pm \sqrt{49-24}}{4} \\ p=\frac{7\pm \sqrt{25}}{4} \\ p=\frac{7\pm 5}{4} \end{gathered}$$

On further simplifying we get

$$\begin{gathered} p=\frac{7+5}{4} \\ p=\frac{12}{4} \\ p=3 \end{gathered}$$and$$\begin{gathered} p=\frac{7-5}{4} \\ p=\frac{2}{4} \\ p=\frac{1}{2} \end{gathered}$$

Conclusion

The solution of the quadratic equation is$p=3$and$p=\frac{1}{2}$