I NEED A REAL ANSWER PLEASE! Find a polynomial that had a leading coefficient of 4 and has the given degree and zeros. Degree 3 with 2, 1/2, and 3/2 as zeros ?x^(3) + {?}x^(2) +…

Question

I NEED A REAL ANSWER PLEASE!

Find a polynomial that had a leading coefficient of 4 and has the given degree and zeros.

Degree 3 with 2, 1/2, and 3/2 as zeros


`?x^(3) + {?}x^(2) + ?x + ?`
​

Answer 1

4x^3-6x^2-6x+9

Explanation:

I would write out the solutions as expressions and expand them:

(x-2)(x-1/2)(x-3/2)

(x^2-1/2x-2x+1)(x-3/2)

(x^2-5/2x+1)(x-3/2)

x^3-(3/2)x^2-(5/2)x+15/4+x-3/2

x^3-(3/2)x^2-(3/2)x+9/4

Next, since the leading coefficient has to be 4x^3, I could just multiply the entire expression by 4:

4x^3-(12/2)x^2-(12/2)x+36/4

4x^3-6x^2-6x+9

Hopefully, this was helpful! Comment below if you would like me to explain further!