Question

What is the answer please.... need help

Answer 1

`f\left(x\right)=x^3-6x^2+3x+10` is the function of the least degree has the real coefficients and the leading coefficients of 1 and with the zeros -1, 5, and 2.

Explanation:

Given the function

`f\left(x\right)=x^3-6x^2+3x+10`

As the highest power of the x-variable is 3 with the leading coefficients of 1.

• So, it is clear that the polynomial function of the least degree has the real coefficients and the leading coefficients of 1.

solving to get the zeros

`f\left(x\right)=x^3-6x^2+3x+10`

`0=x^3-6x^2+3x+10` ∵
`f(x)=0`

as

`Factor\:x^3-6x^2+3x+10\::\:\left(x+1\right)\left(x-2\right)\left(x-5\right)=0`

so

`\left(x+1\right)\left(x-2\right)\left(x-5\right)=0`

Using the zero factor principle

if
`ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)`

`x+1=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:x-5=0`

`x=-1,\:x=2,\:x=5`

Therefore, the zeros of the function are:

`x=-1,\:x=2,\:x=5`

`f\left(x\right)=x^3-6x^2+3x+10` is the function of the least degree has the real coefficients and the leading coefficients of 1 and with the zeros -1, 5, and 2.

Therefore, the last option is true.