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We are given polynomial function f(x)=
We are given two zeros -4 and 5.
Therefore, x=-4 and x=5 is given.
So, the two factors of the polynomial will be (x+4)(x-5).
Let us write some steps to factor the given polynomial.
Let us take above factor (x+4) first.
On factoring (x+4) we get factors
Grouping
Factoring out gcf from each group, we get
So, the final factored form of given polynomial will be
For first to factors (x+4) and (x-5) we have given roots: -4 and 5.
Let us find the root of third factor we got.
Subtracting both sides by 1.
x^2 = - 1.
On taking square root on both sides, we get a square root(-1)
+ i and -i.
Those are imaginary solutions.
Therefore, correct option is B) No, there are two imaginary solutions.