# What are the roots of the equation 5x^2 + 8x - 4 = 0. Do not use quadratic formula

*print*Print*list*Cite

### 2 Answers

Given equation is `5x^2+8x-4=0` . {To factorise `ax^2+bx+c`

we use the criteria that we multiply a and c and then break this number into two parts in such a way that sum of the parts is equal to the coefficient of `x.`

Now this equation we can write as

`5x^2+(10-2)x-4=0`

or, `5x^2+10x-2x-4=0`

or, `(5x^2+10x)-(2x+4)=0`

or, `5x(x+2)-2(x+2)=0`

or, `(5x-2)(x+2)=0`

or, `5x-2=0` and `(x+2)=0`

or, `5x=2` and `x=-2`

or, `x=2/5` and `x=-2`

So the roots of the given quadratic equation are `2/5 and -2.`

The roots of the equation 5x^2 + 8x - 4 = 0 have to be determined.

5x^2 + 8x - 4 = 0

=> 5x^2 + 10x -2x - 4 = 0

=> 5x(x + 2) - 2(x + 2) = 0

=> (5x - 2)(x + 2) = 0

5x - 2

=> x = 2/5

x + 2 = 0

=> x = -2

**The roots of the equation 5x^2 + 8x - 4 = 0 are {-2, 2/5}**