Free Printable Zeroes of polynomials

1.

If $\alpha$ and $\beta$ are the zeroes of a polynomial, such that $\alpha+\beta=6$ and $\alpha\beta=4$ , then write the polynomial

a)

$x^2-6x+4$

b)

$x^2-6x-4$

c)

$x^2+6x+4$

d)

$x^2+6x-4$

2.

Find a quadratic polynomial, whose sum and product of zeroes are $\frac{-8}{3}$ and $\frac{4}{3}$ , respectively.

a)

$3x^2+8x+4$

b)

$3x^2-8x+4$

c)

$x^2+8x+4$

d)

$x^2-8x+4$

3.

The product of the zeroes of $x^3+4x^2+x-6$ is

a)

-4

b)

4

c)

6

d)

-6

4.

If $\alpha,\ \beta\$ and $\gamma$ are zeroes of the polynomial $2x^3+x^2-13x+6$ , then evaluate $\left(\alpha\beta+\beta\gamma+\gamma\alpha\right)$ .

a)

13

b)

-13

c)

$\frac{13}{2}$

d)

$\frac{-13}{2}$

5.

Find the quadratic polynomial whose zeroes are 3 and -4, respectively

a)

$x^2+x+12$

b)

$x^2-x+12$

c)

$x^2+x-12$

d)

$x^2-x-12$

6.

Find a cubic polynomial, whose sum of zeroes, sum of product of zeroes and product of zeroes are -2, -3 and -1 respectively.

a)

$x^3+2x^2-3x-1$

b)

$x^3-2x^2+3x+1$

c)

$x^3-2x^2-3x-1$

d)

$x^3+2x^2-3x+1$

7.

If $\alpha,\ \beta$ are the zeroes of the polynomial $f\left(x\right)=x^2+x+1,$ then find the value of $\frac{1}{\alpha}+\frac{1}{\beta}.$

a)

1

b)

-1

c)

2

d)

-2

8.

For what value of $k,$ $-4$ is a zero of the polynomial $x^2-x-\left(2k+2\right)?$

a)

-9

b)

9

c)

-11

d)

11

9.

If the sum of the zeroes of the polynomial $f\left(x\right)=2x^3-3kx^2+4x-5$ is $6$ , then the value of $k$ is

a)

2

b)

4

c)

-2

d)

-4

10.

If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $p\left(x\right)=x^2-\left(k+6\right)x+2\left(2k-1\right)$ . Find the value of $k$ , if $\alpha+\beta=\frac{\alpha\beta}{2}.$

a)

-8

b)

8

c)

-7

d)

7

Zeroes of polynomials

Total questions: 10

Worksheet time: 7mins

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