The solutions of the quadratic equation \(x^2+px+q=0\) are obtained by adding \(5\) to each of the solutions of \(x^2-4x+2=0\). Find the value of \(3p+q\).
+128399 Call the roots of x^2 - 3x + 2 = 0 = m , n
The roots of x^2 -3x + 2 = 0 sum to -(-3)/1 = 3
The product of the roots = 2
So mn = 2
So (m + 5) + (n + 5) = (m + n) + 10 = 3 + 10 = 13 ....so p = -p/ 1 = -13
And the product of these roots = q
So
(m + 5)(n + 5) = q
mn + 5(m+n) + 25 = q
2 + 5 (3) + 25 = q
42 = q
So
3p + q =
3 (-13) + 42 = 3
