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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