Question

Now, suppose one of the roots of the polynomial function is irrational. The roots of the function are 2, -dn.net/?f=%5Csqrt%7B3%7D" id="TexFormula1" title="\sqrt{3}" alt="\sqrt{3}" align="absmiddle" class="latex-formula">, and 5. Write the equation for this polynomial function.
Which of the following must also be a root of the function?
-$\sqrt{3}$

The equation of the polynomial function is:
f(x)=(x-2)(x-5)(x-$\sqrt{3}$)(x+$\sqrt{3}$)

EXPAND:f(x) = $x^{4}$- _________$x^{3}$+_________$x^{2}$+_________x-__________

Answer 1

answer:

b. -√3

hope this helps! :o)

Answer 2

1.  Since, the roots of the function are 2,$\sqrt{3}$ and 5. We have to write the equation for this polynomial function.

So, the equation is $(x-2)(x-\sqrt3)(x-5)=0$.

2.  Now, the equation of the polynomial function is

$f(x) = (x-2)(x-5)(x-\sqrt3)(x+\sqrt3)$

We have to find its expanded form.

we will proceed from step by step to find the expanded form.

$(x-2)(x-5)(x-\sqrt3)(x+\sqrt3)$

= $[(x-2)(x-5)][(x-\sqrt3)(x+\sqrt3)]$

= $[x^2-7x+10][x^2-3]$

=$(x^4-7x^3+10x^2-3x^2+21x-30)$

= $x^4-7x^3+7x^2+21x-30$

So, the expanded form of the given polynomial function is:

f(x) = = $x^4-7x^3+7x^2+21x-30$.