Further Pure 1 AQA Roots and Coefficients Of A Quadratic Equation

α + β = -b/a

αβ = c/a

where ax^2+bx+c=0

x^2 - (sum of roots)x + (products of roots) = 0

The quadratic equation 3x^2+9x-11=0 has roots α and β. Find the equation whose roots are α + β and αβ.

α + β=-3 and αβ=-11/3

 The sum of the new roots is α + β + αβ = -3 -11/3 = -20/3

The product of the new roots is: (α + β) X αβ = -3 X -11/3 = 11

Therefore, the new equation is: 3x^2+20x+33=0