Roots of Polynomials Quadratics If the roots of the quadratic equation are  and  then the factorised equation is : (x –  )(x –  ) = 0 (x –  )(x –  ) = x 2 – (  +  )x  x 2 - (sum of roots)x + (product of roots) = 0 (x –  )(x –  ) = x 2 –3x –2x 

Roots of Polynomials Quadratics If the roots of the quadratic equation are -  and  then the factorised equation is : (x +  )(x –  ) = 0 (x +  )(x –  ) = x 2 + 2x -5x  x 2 - (sum of roots)x + (product of roots) = 0 (x +  )(x –  ) = x 2 – (– 2 + 5)x 

Roots of Polynomials Quadratics If the roots of the quadratic equation are  and  then the factorised equation is : If the equation is of the form ax 2 + bx + c = 0then divide by `a` so that the coefficient of x 2 is 1 x 2 +  x 2 - (sum of roots)x + (product of roots) = 0 (x –  )(x –  ) = 0 (x –  )(x –  ) = x 2 – (  +  )x  x 2 - (sum of roots)x + (product of roots) = 0 Sum of roots =  = Product of roots =  = LEARN

These results enable us to find other quadratic equations which are related to the original given equation. x 2 – 3x – 5 = 0 Find 1)  2)  3)    2 and (  ) 2 4) Equation with roots  2 and  2 5) Using x 2 - (sum of roots)x + (product of roots) = 0 then the new equation is: x 2 – 19x + 25 = 0 1)  2  3                 i.e Product of new roots i.e Sum of new roots         

Ex.2 6x 2 + 2x – 3 = 0 Find 1  2)  3) Equation with roots and   and   1)  2)  3) Sum of new roots =  Product of new roots =  

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