If the roots of the equation 3x^2 - 6x + 5 = 0 are a and b, then find the quadratic whose roots are a + b and 2/(a + b).
+128408 By Vieta
To avoid confusion......let m and n be the roots
The form is ax^2 + bx + c where a = , b = -6
Sum of the roots = m + n = -b/a = - ( - 6 ) / 3 = 2
So......in our new quadratic....let a = 1
(m + n) + 2 / ( m + n) = 2 + 2 / 2 = 2 + 1 = 3 = -b → -3 = b
And the product of the roots = c = (m + n) * 2 / (m + n ) = 2
The quadratic is ax^2 + bx + c = x^2 - 3 x + 2
