Question

What is the sum of 20x^2-10x-30

Answer 1

The sum of the roots is 0.5

Explanation:

The correct question is

What is the sum of the roots of 20x^2-10x-30

we know that

In a quadratic equation of the form

`ax^(2) +bx+c=0`

The sum of the roots is equal to

`-\frac{b} {a}`

in this problem we have

`20x^(2) -10x-30=0`

so

`a=20\\b=-10\\c=-30`

substitute

`-\frac{(-10)} {20}=0.5`

Verify

Find the roots of the quadratic equation

The formula to solve a quadratic equation is equal to

`x=\frac{-b\pm\sqrt{b^(2)-4ac}} {2a}`

`a=20\\b=-10\\c=-30`

substitute

`x=\frac{-(-10)\pm\sqrt{-10^(2)-4(20)(-30)}} {2(20)}`

`x=\frac{10\pm√(2,500)} {40}`

`x=\frac{10\pm50} {40}`

`x=\frac{10+50} {40}=1.5`

`x=\frac{10-50} {40}=-1`

The roots are x=-1 and x=1.5

The sum of the roots are

`-1+1.5=0.5` ----> is ok