Answer:
The sum of the roots is 0.5
Step-by-step 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
[tex]ax^{2} +bx+c=0[/tex]
The sum of the roots is equal to
[tex]-\frac{b} {a}[/tex]
in this problem we have
[tex]20x^{2} -10x-30=0[/tex]
so
[tex]a=20\\b=-10\\c=-30[/tex]
substitute
[tex]-\frac{(-10)} {20}=0.5[/tex]
Verify
Find the roots of the quadratic equation
The formula to solve a quadratic equation is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
[tex]a=20\\b=-10\\c=-30[/tex]
substitute
[tex]x=\frac{-(-10)\pm\sqrt{-10^{2}-4(20)(-30)}} {2(20)}[/tex]
[tex]x=\frac{10\pm\sqrt{2,500}} {40}[/tex]
[tex]x=\frac{10\pm50} {40}[/tex]
[tex]x=\frac{10+50} {40}=1.5[/tex]
[tex]x=\frac{10-50} {40}=-1[/tex]
The roots are x=-1 and x=1.5
The sum of the roots are
[tex]-1+1.5=0.5[/tex] ----> is ok
