. Find a polynomial of degree 3 whose zeros are -4, -1, 2 and y intercept 16.

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Chapter4: Polynomial And Rational Functions
Section4.5: Zeros Of Polynomial Functions
Problem 79E
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1. Find a polynomial of degree 3 whose zeros are -4, -1, 2 and y intercept 16.
2. Find a polynomial of degree 5 whose zeros are -4, 2, 0 (multiplicity 3) and contains the point (-2, 64).
3. Find a polynomial of degree 4 whose coefficients are real numbers and that has the zeros -1, 2 and -4 - i.
4. Find all the zeros of f(x)=x* – x* – 4x³ +8x² – 32x+ 48 by using synthetic division. Write f(x) in
factored form.
5. Find all the zeros of f(x)= 2x* + 2x' – 1 lx² + x - 6 by using synthetic division. Write f(x) in
factored form.
x²(3 + x)(x+4)
6. Solve the inequality
> 0 algebraically and graph the solution set.
(x+5)(x – 1)
(3 – x)' (2x + 1)
x³ – 1
7. Solve the inequality
<0 algebraically and graph the solution set.
8. Let f(x)= 2x² +5 and g(x)=3x+a . Find a so that the graph of fog crosses the y axis at 23.
x² - 4
;x > 0 and verify your answer. Also fine the domain and range of
2x?
9. Find the inverse of f(x) =
the inverse function.
10. Let f(x)= log, (x–1) – 3
(i) what is the domain of f(x)?
(ii) Find the zero of f(x).
(iii) If f(x)=-1, what is x? What point is on the graph of f(x)?
11. Solve:
(x² +x)–log (x – x) = -1
12. Solve: log, (x+1)–log, x =1
Transcribed Image Text:1. Find a polynomial of degree 3 whose zeros are -4, -1, 2 and y intercept 16. 2. Find a polynomial of degree 5 whose zeros are -4, 2, 0 (multiplicity 3) and contains the point (-2, 64). 3. Find a polynomial of degree 4 whose coefficients are real numbers and that has the zeros -1, 2 and -4 - i. 4. Find all the zeros of f(x)=x* – x* – 4x³ +8x² – 32x+ 48 by using synthetic division. Write f(x) in factored form. 5. Find all the zeros of f(x)= 2x* + 2x' – 1 lx² + x - 6 by using synthetic division. Write f(x) in factored form. x²(3 + x)(x+4) 6. Solve the inequality > 0 algebraically and graph the solution set. (x+5)(x – 1) (3 – x)' (2x + 1) x³ – 1 7. Solve the inequality <0 algebraically and graph the solution set. 8. Let f(x)= 2x² +5 and g(x)=3x+a . Find a so that the graph of fog crosses the y axis at 23. x² - 4 ;x > 0 and verify your answer. Also fine the domain and range of 2x? 9. Find the inverse of f(x) = the inverse function. 10. Let f(x)= log, (x–1) – 3 (i) what is the domain of f(x)? (ii) Find the zero of f(x). (iii) If f(x)=-1, what is x? What point is on the graph of f(x)? 11. Solve: (x² +x)–log (x – x) = -1 12. Solve: log, (x+1)–log, x =1
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