Question

4. Use the “zero” utility of your calculator to determine the zeros of f(x) = x^2 + 5x - 10 (round to the nearest tenth if necessary).

5. What are the zeros of the polynomial f(x) = x^4 (x-2)^2 (x+1)? Tel whether each zero is odd or even.

7. Use synthetic division to determine if k = -3 is a zero of f(x) = 2x^3 + 13x ^2 + 30x + 25. Give the answer as “yes” or “no”. Show your work

8.) Use synthetic division to determine if x-1 is a factor of x^3 + 4x^2 + x - 6. Give the answer as “yes” or “no”. Show your work

Answer 1

1) Given function is f(x) = x² + 5x - 10

Now, f(x) = 0 gives, x² + 5x - 10 = 0

i.e., x =

i.e., x =

i.e., x =

i.e., x 1.5, -6.5

Therefore, the zeros of the given function are 1.5 and -6.5

2) Given function is f(x) = x⁴(x-2)²(x+1).

Now, f(x) = 0 gives, x⁴(x-2)²(x+1) = 0

i.e., x =0,-1,2

Here 0,2 are even zeros and -1 is odd zero.

3) We have to check here whether x = -3 is a zero of f(x) = 2x³+13x²+30x+25 or not.

Putting x = -3 in the given function we get, f(-3) = 2(-3)³+13(-3)²+30(-3)+25

i.e., f(-3) = -54+117-90+25

i.e., f(-3) = -2

Therefore, -3 is not a zero of the given function.

4) We have to check here whether x-1 is a factor of f(x) = x³+4x²+x-6 or not.

Dividing f(x) by x-1 we get, (x³+4x²+x-6)/(x-1) = x²+5x+6 and there is no remainder.

Therefore, x-1 is a factor of the given function.