Question

if one zero of a quadratic polynomial I 8 and the product of the zeroes is -56,then the quadratic polynomial is​

Answer 1

GIVEN: One of the zeroes of the polynomial (α)= 18

             Product of the zeroes(α X β) = -56

TO FIND:  The quadratic equation.

SOLUTION:

              As one of the root α is given and the sum of the roots is -56.

 So, the other root of the equation=> (α×β) = -56

                                                         =>  18×β = -56

                                                         =>  β= -56/18

                                                         =>  β= -28/9

Now, to find out the equation of the equation we need the sum of the roots.

             α+β=18+(-28/9)

             9(α+β) =162-28

             9(α+β) = 134

              (α+β) = 134/9

So, now by using the sum and the product of the roots we can easily find the equation.

                   so the equation = $x^{2}$ - (α+β)$x^{1}$ + αβ = 0

hence, the quadratic equation is $x^{2}$ -(134/9)$x^{1}$ + (-56) = 0

                                                    =>$x^{2}$ - 134/9 $x^{1}$ -56 = 0

                                                    =>9$x^{2}$ - 134$x^{1}$ - 56 = 0

                SO, the Quadratic equation is 9$x^{2}$ - 134$x^{}$ - 56 = 0