Question

Find the solution to the equation below.2x²+3x-20=0

Answer 1

Step-by-step explanation

We are asked to solve the given quadratic equation

`2x^2+3x-20=0`

To do so, we will have to find the factors of the product of the coefficient of the first and last term whose sum is 3

Thus

`2*-20=-40`

So the factor of -40 which also gives a sum of 3 will be

`8\text{ and -5}`

Thus

`\begin{gathered} 2x^2+8x-5x-20=0 \\ 2x(x+4)-5(x+4)=0 \\ (2x-5)(x+4)=0 \end{gathered}`

We will have the answer will be

`(2x-5)(x+4)`

Simplifying further

we will have the zeros to be

`\begin{gathered} 2x-5=0 \\ x=(5)/(2)=2.5 \\ \\ \end{gathered}`

Also

`\begin{gathered} x+4=0 \\ x=-4 \end{gathered}`

So the answers are:

x = -4 and x= 5 over 2