Let x^2+bx+c=0 be a quadratic whose roots are each two more than the roots of 3x^2-5x-17. What is c?
+128474 Call the roots of the second quadratic m and n
The product of these roots = -17/3 = mn
And the sum of the roots = m + n = 5/3 ⇒ 2 (m + n) = 10/3
So...in the polynomial of interest the product of the roots = (m + 2) (n + 2) = c
So
mn + 2 (m + n) + 4 = c
-17/3 + 10/3 + 4 = c
-7/3 + 4 = c
-7/3 + 12/3 = c
5/3 = c
