Question

Select the two values of x that are roots of this equation.
2x - 3 = -5x2

Answer 1

Answer
2x and -5x
Because it’s the only 2 numbers that have x’s in them

Answer 2

x = -1 or x =
`(3)/(5)`

Explanation:

2x - 3 = -5x²

This is a quadratic form of equation.

We will start by rearranging the equation, we will move all the variable to the left-hand side of the equation, which means the right-hand side of the equation will become zero.

Add 5x² to both-side of the equation

2x - 3 + 5x² = -5x² + 5x²

2x - 3 + 5x² = 0

5x² + 2x -3 = 0

Now we can now proceed to solve;

Find two factors such that it sum will give 5 and its product will give -15

The two numbers are 5 and -3 (That is 5×-3 = -15 and 5 +(-3)=2)

We will replace 2x by 5x and -3x

So that our equation becomes;

5x² + 5x -3x-3 = 0

We will now factorize

( 5x² + 5x) (-3x -3 )= 0

On the first bracket, 5x is common and so it will be factored out and on the second bracket -3 is common and so it will be factored out

5x(x + 1) -3(x + 1) = 0

(x+1)(5x-3) = 0

Either x +1 = 0 ⇒ x = -1

or

5x - 3 = 0

5x = 3

x =
`(3)/(5)`