Question

When solved for x, what is the sum when the roots of the quadratic equation are added?

x^2 + 10x + 24 = 0
A) −10
B) −12
C) 10
D) 12

Answer 1

Option A.
`-10`

Explanation:

we know that

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

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

in this problem we have

`x^(2) +10x+24=0`

so

`a=1\\b=10\\c=24`

substitute in the formula

`x=\frac{-10(+/-)\sqrt{10^(2)-4(1)(24)}} {2(1)}`

`x=\frac{-10(+/-)√(4)} {2}`

`x=\frac{-10(+/-)2} {2}`

`x=\frac{-10(+)2} {2}=-4`

`x=\frac{-10(-)2} {2}=-6`

The roots are -4 and -6

Find the sum

`-4-6=-10`