URGENT!! The difference between the roots of the quadratic equation x2−12x+q=0 is 2. Find q

q=35

Step-by-step explanation:

x2 - 12x + q = 0

Let the two roots be r and r+2.

Factor the quadratic expression:

(x - r)[x - (r + 2)] = 0

Expand, simplify, group like terms, and get

x2 - 2(r + 1)x + r(r + 2) = 0

Compare to

x2 - 12x + q = 0

and set equal the coefficients of like terms:

Coefficient of x:

-2(r + 1) = -12 ⇒ r + 1 = 6 ⇒ r = 5

(Then the other root is r + 2 = 5 + 2 = 7)

Constant term:

r(r + 2) = q ⇒ 5(5 + 2) = q

q = 35

Test the solution:

(x - 5)(x - 7) = x2 - 12x + 35

With two roots differing by 2, you get an equation of the form

x2 - 12x + q = 0

with q = 35.