Polynomials Practice 3: Construct and Reason

Section A: Build Polynomials

Question 1mcq

Form a monic quadratic polynomial whose zeros are

2

and

5

.

A.

x^2+7x+10

B.

x^2-10x+7

C.

x^2-7x+10

D.

2x^2-5x+10

Question 2mcq

Which polynomial has the same zeros as

x^2-3x+2

?

A.

x^2+3x+2

B.

x^2-3x+4

C.

2x^2-3x+2

D.

2x^2-6x+4

Question 3mcq

Find a quadratic polynomial whose sum of zeros is

6

and product is

8

.

A.

x^2+6x+8

B.

x^2-6x+8

C.

x^2-8x+6

D.

x^2+8x-6

Question 4mcq

A garden path model has zeros

-1

and

4

. Which polynomial could represent it?

A.

x^2+3x-4

B.

x^2-4x-1

C.

x^2+4x+1

D.

x^2-3x-4

Question 5mcq

Why do

x^2-5x+6

and

3x^2-15x+18

have the same zeros?

A.The second is

3

times the first.

B.They have the same degree only.

C.Their constant terms are both positive.

D.All quadratics have the same zeros.

Section B: Reason and Repair

Question 6mcq

If one zero of

x^2+kx+12

is

3

, what is

k

?

A.

7

B.

4

C.

-7

D.

-4

Question 7mcq

If the sum of zeros of

2x^2-ax+8

is

5

, find

a

.

A.

-10

B.

5

C.

16

D.

10

Question 8mcq

A student says product of zeros of

4x^2-9x+2

is

\fracrac{9}{4}

. What did they do?

A.They used

-\fracrac{b}{a}

instead of

\fracrac{c}{a}

.

B.They used the constant term correctly.

C.They multiplied the zeros directly.

D.They changed the degree.

Question 9mcq

Assertion: The product of zeros of

-2x^2+5x+3

is

-\fracrac{3}{2}

. Reason: Product of zeros is

\fracrac{c}{a}

.

A.Both true, but unrelated.

B.Assertion true, reason false.

C.Both are true, and the reason explains the assertion.

D.Assertion false, reason true.

Question 10mcq

The zeros of

kx^2+4x+1

have product

\fracrac{1}{3}

. What is

k

?

A.

\fracrac{1}{3}

B.

3

C.

4

D.

12