Polynomials Practice 2: Graphical Zeros and Relations

Section A: Graph and Table Reading

Question 1mcq

A graph of

y=p(x)

crosses the

x

-axis at

x=-2

and

x=5

. What are the zeros?

A.

2

and

-5

B.

-2

and

5

C.

0

and

5

D.

-2

only

Question 2mcq

If a polynomial graph does not touch or cross the

x

-axis, how many real zeros are visible?

A.

1

B.

2

C.Cannot be less than

1

D.

0

Question 3mcq

A U-shaped graph touches the

x

-axis at

x=3

and turns back. How many distinct real zeros does it have?

A.

1

B.

0

C.

2

D.

3

Question 4mcq

A quadratic graph cuts the

x

-axis at two points. What can you say about its real zeros?

A.It has no real zeros.

B.It has exactly one real zero.

C.It has two distinct real zeros.

D.It has infinitely many zeros.

Question 5mcq

For

p(x)=2x^2-7x+3

, the sum of zeros is:

A.

-\fracrac{7}{2}

B.

\fracrac{3}{2}

C.

-3

D.

\fracrac{7}{2}

Section B: Coefficient Relations

Question 6mcq

For

p(x)=3x^2+5x-2

, the product of zeros is:

A.

-\fracrac{2}{3}

B.

\fracrac{2}{3}

C.

\fracrac{5}{3}

D.

-\fracrac{5}{3}

Question 7mcq

Zeros of

x^2-4x+3

are

1

and

3

. Which verification is correct?

A.Sum

=-4

and product

=-3

B.Sum

=3

and product

=4

C.Sum

=4=-\fracrac{-4}{1}

and product

=3=\fracrac{3}{1}

D.Sum

=1

and product

=3

Question 8mcq

If the zeros of a quadratic polynomial are

-4

and

6

, what is the sum of zeros?

A.

-2

B.

2

C.

24

D.

-24

Question 9mcq

If the zeros are

-4

and

6

, what should

\fracrac{c}{a}

be?

A.

-24

B.

24

C.

2

D.

-2

Question 10mcq

A student says the sum of zeros of

5x^2+2x-1

is

\fracrac{2}{5}

. What is the mistake?

A.They used

\fracrac{c}{a}

instead of sum.

B.They forgot the negative sign in

-\fracrac{b}{a}

.

C.They divided by

c

.

D.The polynomial is not quadratic.