Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition.

−5, 2, 1; f(3) = 64

f(x) =

−5, 2, 1; f(3) = 64

f(x) =

Arthur Pratt
2021-12-15
Answered

Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition.

−5, 2, 1; f(3) = 64

f(x) =

−5, 2, 1; f(3) = 64

f(x) =

You can still ask an expert for help

veiga34

Answered 2021-12-16
Author has **32** answers

Step 1

here we use the linear factors for the zeroes given

see below the calculation

Step 2

Given zeros are −5,2,1

then the linear factor that divide the polynomial f(x) are (x+5),

(x-2),(x-1)

then f(x)=m(x+5)(x-2)(x-1) but to satisfy the another conditions that f(3)=64

we see that f(3)=m(3+5)(3-2)(3-1)=12m

then 12m=64 we get$m=\frac{16}{3}$

then required 3 degree polynomial is$f\left(x\right)=\frac{16}{3}(x+5)(x-2)(x-1)$

$=\frac{16}{3}({x}^{3}+2{x}^{2}-13x+10)$

here we use the linear factors for the zeroes given

see below the calculation

Step 2

Given zeros are −5,2,1

then the linear factor that divide the polynomial f(x) are (x+5),

(x-2),(x-1)

then f(x)=m(x+5)(x-2)(x-1) but to satisfy the another conditions that f(3)=64

we see that f(3)=m(3+5)(3-2)(3-1)=12m

then 12m=64 we get

then required 3 degree polynomial is

Pansdorfp6

Answered 2021-12-17
Author has **27** answers

Given zeroes -5,2,1

Equation of polynomial

f(x)=k(x-(-5))(x-2)(x-1)

=k(x+5)(x-2)(x-1)

$=k({x}^{2}-2x+5x-10)(x-1)$

$=k({x}^{2}+3x-10)(x-1)$

$=k({x}^{3}-{x}^{2}+3{x}^{2}-3x-10x+10)$

$=k({x}^{3}+2{x}^{2}-13x+10)$

$\therefore f\left(x\right)=k({x}^{3}+2{x}^{2}-13x+10)$

Given f(3)=64

$\therefore k({3}^{3}+2x{3}^{2}-13x3+10)=64$

$\Rightarrow k(27+18-39+10)=64$

$\Rightarrow 16k=64$

$\Rightarrow k=\frac{64}{16}-4$

$\therefore f\left(x\right)=4({x}^{3}+2{x}^{2}-13x+10)$

Equation of polynomial

f(x)=k(x-(-5))(x-2)(x-1)

=k(x+5)(x-2)(x-1)

Given f(3)=64

asked 2021-06-03

Determine whether the following function is a polynomial function. If the function is a polynomial function, state its degree. If it is not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.

$g(x)=3-\frac{{x}^{2}}{4}$

asked 2021-12-17

Find the roots of the given quadratic equation by factorization method

${x}^{2}-3x-10=0$

asked 2020-11-22

Decide whether $z\left(\sqrt{-5}\right)$ unique factorization domain or not (ring theory)

asked 2022-02-11

How would you multiply (x+8)(x-8)?

asked 2022-02-01

What is the standard form of $y=(x+2){(2x-3)}^{2}$ ?

asked 2021-12-13

Find the LCM of the given polynomial.

${x}^{2}-4,{x}^{2}-x-2$

asked 2022-02-03

How do you foil (-4x+5)(-2x-3)?