**Polynomial functions worksheet for grade 11**

Here we are going to see some practice questions on polynomial functions.

(1) Find the zeros of the polynomial function f(x) = 4x^{2} − 25.

(2) If x = −2 is one root of x^{3} − x^{2} − 17x = 22, then find the other roots of equation.

(3) Find the real roots of x^{4} = 16.

(4) Solve (2x + 1)^{2} − (3x + 2)^{2} = 0

**Question 1 :**

Find the zeros of the polynomial function f(x) = 4x^{2} − 25.

**Solution :**

f(x) = 0

4x^{2} − 25 = 0

4x^{2} = 25

x^{2} = 25/4

x = √(25/4)

x = ±5/2

x = 5/2 or -5/2

**Question 2 :**

If x = −2 is one root of x^{3} − x^{2} − 17x = 22, then find the other roots of equation.

**Solution :**

Given that : x^{3} − x^{2} − 17x = 22

x^{3} − x^{2} − 17x - 22 = 0

One root of the given polynomial is x = -2

From this, we may find the factor (x + 2)

By using synthetic division, we may find other two factors.

So, the factors are (x + 2) (x^{2} − 3x - 11)

By solving x^{2} − 3x - 11, we may get other two values.

x = [-b ± √(b^{2} - 4ac)] / 2a

a = 1, b = -3 and c = -11

x = [3 ± √(3^{2} - 4(1)(-11))] / 2(1)

x = [3 ± √(9 + 44)] / 2

x = [3 ± √53] / 2

Hence the other roots are (3 + √53)/2 and (3 + √53)/2.

**Question 3 :**

Find the real roots of x^{4} = 16.

**Solution :**

x^{4} = 16

x^{4} = 2^{4}

x = ±2

**Question 4 :**

Solve (2x + 1)^{2} − (3x + 2)^{2} = 0

**Solution :**

(2x + 1)^{2} − (3x + 2)^{2} = 0

Expanding the above expression using algebraic identities, we get

(2x + 1) + (3x + 2) = 0 (or) (2x + 1) - (3x + 2) = 0

2x + 3x + 1 + 2 = 0 5x + 3 = 0 x = -3/5 |
2x - 3x + 1 - 2 = 0 -x - 1 = 0 -x = 1 x = -1 |

Hence the solutions are -3/5 and -1.

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