the difference of the roots of a quadratic equation is 6 find c.

Question

x²+x+c=0

 

Answer 1

Let r and s be the roots of the quadratic equation with r > s. Then r+ s = -1 and we are given that r - s = 6. Adding these two equations gives us that 2r = 5, and so r = 5/2. From the first equation, we get s= -1 - r = -1 - 5/2 = -2/2 - 5/ 2 = -7/2. Finally, we have c= rs = (5/2)(-7/2) = -35/4.

 

Note: The sum of the roots of the quadratic equation x² + bx + c = 0 is -b and the product of the roots is c.