Finding zeros of polynomial functions worksheet with answers

(1)  Find the value of the polynomial 

f(y)  =  6y - 3y2 + 3 at 

(i) y  =  1 (ii)  y  =  -1  (iii)  y  =  0         Solution

(2)  If p(x) = x2 – 2√2 x + 1, find p(2√2)     Solution

(3)  Find the zeroes of the polynomial in each of the following :

(i)  p(x)  =  x - 3

(ii) p(x) = 2x + 5

(iii) q(y) = 2y – 3

(iv)  f(z)  =  8z 

(v) p(x)  =  ax, when a ≠ 0 

(vi) h(x) = ax + b, a ≠ 0, a,b ∈ R         Solution

(4)  Find the roots of the polynomial equations.

(i) 5x – 6 = 0

(ii) x + 3 = 0

(iii) 10x + 9 = 0

(iv) 9x – 4 = 0         Solution

(5)  Verify whether the following are zeros of the polynomial indicated against them, or not.

(i)  p(x)  =  2x - 1, x = 1/2

(ii)  p(x)  =  x3 - 1, x  =  1

(iii)  p(x)  =  ax + b, x = -b/a

(iv)  p(x)  = (x + 3) (x - 4), x = 4, x = –3     Solution

(6)  Find the number of zeros of the following polynomials represented by their graphs.

Solution

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Related Topics:
More Lessons for PreCalculus
Math Worksheets

Videos, worksheets, examples, solutions, and activities to help PreCalculus students learn how to find the zeros or roots of a polynomial function.

The following figure show how to find the zeros or roots of a polynomial function Graphically or using the Rational Zeros Theorem. Scroll down the page for more examples and solutions.

Find the Zeros of a Polynomial Function - Integer Zeros
This video provides an introductory example of how to find the zeros of a degree 3 polynomial function.
Example:
Find all the zeros or roots of the given function graphically and using the Rational Zeros Theorem.
f(x) = x3 - 3x2 - 13x + 15

• Show Step-by-step Solutions

Find the Zeros of a Polynomial Function - Real Rational Zeros

This video provides an example of how to find the zeros of a degree 3 polynomial function with the help of a graph of the function.
Example:
Find all the zeros or roots of the given function.
f(x) = 6x3 - 11x2 - 26x + 15

• Show Step-by-step Solutions

Find the Zeros of a Polynomial Function with Irrational Zeros
This video provides an example of how to find the zeros of a degree 3 polynomial function with the help of a graph of the function. The function as 1 real rational zero and 2 irrational zeros.
Example:
Find all the zeros or roots of the given function.
f(x) = x3 - 4x2 - 11x + 2

• Show Step-by-step Solutions

Zeros of Polynomial Functions
How to use the graphing calculator to find real zeros of polynomial functions?
Example:
Find all the zeros or roots of the given function.
f(x) = 3x4 - 4x3 - 11x2 + 16x - 4

• Show Step-by-step Solutions

Finding the Zeros of a Polynomial Function
A couple of examples on finding the zeros of a polynomial function.
Example:
Find all the zeros or roots of the given functions.
f(x) = 3x3 - 19x2 + 33x - 9
f(x) = x3 - 2x2 - 11x + 52

• Show Step-by-step Solutions

Graphing polynomials in factored form
Graphing polynomials in factored form taking into account multiplicities of zeros.
Example:
Graph y = -3.5x2(x - 4)3(x + 3)

• Show Step-by-step Solutions

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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