f(x) = [tex] x^{4} [/tex]- _________[tex] x^{3} [/tex]+_________[tex] x^{2} [/tex]+_________x-__________
1. Since, the roots of the function are 2,[tex]\sqrt{3}[/tex] and 5. We have to write the equation for this polynomial function.
So, the equation is [tex](x-2)(x-\sqrt3)(x-5)=0[/tex].
2. Now, the equation of the polynomial function is
[tex]f(x) = (x-2)(x-5)(x-\sqrt3)(x+\sqrt3)[/tex]
We have to find its expanded form.
we will proceed from step by step to find the expanded form.
[tex](x-2)(x-5)(x-\sqrt3)(x+\sqrt3)[/tex]
= [tex][(x-2)(x-5)][(x-\sqrt3)(x+\sqrt3)][/tex]
= [tex][x^2-7x+10][x^2-3][/tex]
=[tex](x^4-7x^3+10x^2-3x^2+21x-30)[/tex]
= [tex]x^4-7x^3+7x^2+21x-30[/tex]
So, the expanded form of the given polynomial function is:
f(x) = = [tex]x^4-7x^3+7x^2+21x-30[/tex].
