Find The Sum Of The Roots Of The Quadratic x^2+7x-13. Help, Please?

2 Answers
Sean
Dec 21, 2017

-7

Explanation:

.

x^2+7x-13

We can use the quadratic formula to solve for the roots of:

ax^2+bx+c=0

x=(-b+-sqrt(b^2-4ac))/(2a)

In our problem, a=1, b=7, c=-13

x=(-7+-sqrt(7^2-4(1)(-13)))/(2(1))=(-7+-sqrt(49+52))/2

x=-7/2+sqrt101/2, and

x=-7/2-sqrt101/2

These are the two roots. If we add them together we get the sum of the roots:

-7/2+sqrt101/2-7/2-sqrt101/2=-14/2=-7

Jim G.
Dec 21, 2017

-7

Explanation:

" if "alpha" and "beta" are the roots of the equation"

ax^2+bx+c=0" then"

(x-alpha)(x-beta)=0

rArrx^2-x(alpha+beta)+alphabeta=0

"comparing this equation with"

ax^2+bx+c=0to(x^2+b/ax+c/a=0)

rArralpha+beta=-b/a" and "alphabeta=c/a

"for "x^2+7x-13=0larra=1,b=7

rArralpha+beta=-7/1=-7

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