Question

find all the zeroes of polynomials x3+5x2-9x-45

Answer 1

Heya user,

A common approach would be to factorize but let's say, we avoid that for the cubic polynomial...

By Hit and Trial,
---> f(3) = 0; which implies ( x - 3 ) is a factor of given polynomial...

Hence, dividing by ( x - 3 ), we obtain the quadratic polynomial as:->
-----> x^2 + 8 x + 15;
===> ( x + 3 ) ( x + 5 );
Hence, By factor theorem, we obtain the zeroes as +3, -3 and -5.....

Answer 2

Given x^3 + 5x^2 - 9x - 45 can be written as

          x^2(x + 5) -9(x + 5) = 0

         (x + 5)(x^2 - 9) = 0

        x + 5 = 0 = > x = -5

       x^2 - 9 = 0 = > x = 3,-3.

Therefore, all the zeroes of the polynomial are -5, 3, -3.


Hope this helps!