Question

How do you solve `-5x^2 + 10x + 15 = 0`?

Answer 1

`x=-1 or x=3`

Explanation:

`-5x^2+10x+15=0`
`=-5(x^2-2x-3)=0`
To factorize the polynomial `x^2-2x-3` in the form `(x+a)(x+b)`
we have to find two integers `a` and `b` such that
`a+b=-2` and `a*b=-3`

check for `a=1` and `b=-3`
so,`color(blue)((x^2-2x-3)=(x+1)(x-3))`

`-5x^2+10x+15=0`
`rArr-5(x+1)(x-3)=0`

Knowing that if the product is zero then one of the factors can be equal to zero .

Since `-5!=0`
Therefore,

`x+1=0`
`x=-1`

Or,
`x-3=0`
`x=3`