The difference between the roots of the quadratic equation x2−14x+q=0 is 6. find q.

Step-by-step explanation:

In a quadratic equation, a rule known as Vieta's Theorem tells us that roots 1 and 2 (we'll call them x1 and x2) added up is equal to -b/a, and x1 multiplied by x2 is equal to c/a.  because x1-x2 is 6, and x1+x2=-b/a, which is -(-14), or 14, we can use the substitution method to find out the roots of the equation, being 4 and 10. When putting these roots into the equation, we get that 4^2-14(4)+q=0, and 10^2-14(10)+q=0. We can simplify these equations to make -40+q=0, and adding 40 on both sides gets us that q=40.

To recap:

Vieta's Formula:

use substitution to find the roots

enter the roots into the quadratic equation

solve the equation!

q = 40

i don't see any steps below, sweetheart