Further Pure 1 AQA Roots and Coefficients Of A Quadratic Equation

Roots of a quadratic equation

Symmetrical functions of roots

Equations with related roots

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  • Created by: Chloe
  • Created on: 04-04-12 18:13

Roots 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 anαβ=-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

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