Question

x4+2x3-26x2+54x-27 given polynomials zero are 3√3 and -3√3.find out the other zero​

Answer 1

Explanation:

Given x=3root3,3root3

=[x-(3root3)][x-(-3root3)] is a factor of p(x) {°.° By rearranging}

=[x-3root3][x+3root3] is a factor of p(x) {Also [(a-b)(a+b)=(a^2-b^2)] }

=[(x)^2 -(3root3)^2] is a factor of p(x) ( Using above identity)

=[(x^2)-27] is a factor of p(x)

Here we have factor as g(x)=[x^2 - 27 ]

To find other two zeroes =[p(x)]÷g(x)]

On dividing it we will remain with r(x) =0 and q(x) in the form of quadratic equation i.e., ax^2+bx+c=0

So we can use middle term splitting or quadratic formula to solve that quadratic equation and we will get other two values of x by it and that will be the other two roots of p(x).

Q.E.D