FINDING REMAINING ZEROS OF POLYNOMIAL FUNCTIONS WORKSHEET

Problem 1 :

If 1 is a zero of the polynomial

p(x) = ax² - 3(a - 1)x - 1

then find the value of 'a' and find other zero.?

Solution

Problem 2 :

What number should be added to the polynomial

x² - 5x + 4

so that 3 is the zero of the polynomial?

Solution

Problem 3 :

If one of the zeros of the cubic polynomial

x³ + ax² + bx + c is -1

then what will be the product of the other two zeros?

Solution

Problem 4 :

Obtain all other zeros of the polynomial

2x⁴ - 9x³+ 5x² + 3x - 1

if two of its zeros are 2 - √3 and 2 + √3?

Solution

Problem 5 :

Find the zeros of the polynomial

f(x) = x³ - 5x² -2x +24

if it is given that the product of its two zeros is 12?

Solution

Problem 6 :

If the zeros of the polynomial f(x) = x³ – 3x² - 6x + 8 are of the form a-b, a, a+b, then find all the zeros.

Solution

Problem 7 :

If α, β are the two zeros of the polynomial

f(y) = y² - 8y + a and α² + β² = 40

find the value of ‘a’?

Solution

Answer Key

1)  another zero is -1

2)  2 is the value to be added.

3)  a - b + c = 1

4)  remaining zeroes are -1/2 and 1.

5)  zeroes are 3 and 4

6)  zeroes are -2, 1 and 4.

7)  a = 12