FIND THE CUBIC POLYNOMIAL WITHE GIVEN ZEROES WORKSHEET

Problem 1 :

Find all the zeroes of the polynomial x3 + 3x2 – 2x – 6, if two of its zeroes are -√2 and √2.

Solution

Problem 2 :

Find all the zeroes of the polynomial 2x3 + x2 – 6x – 3, if two of its zeroes are -√3 and √3.

Solution

Problem 3 :

Obtain all other zeroes of the polynomial 2x3 - 4x – x2 + 2, if two of its zeroes are √2 and -√2.

Solution

Problem 4 :

If the polynomial 6x4 + 8x3 + 17x2 + 21x + 7 is divided by another  polynomial 3x2 + 4x + 1 then the remainder comes out to be ax + b, find ‘a’ and ‘b’. 

Solution

Answer Key

1) All the zeroes are -√2, √2 and -3

2)  All the zeroes are -√3, √3 and -1/2.

3)  All the zeroes are - √2, -√2 and 1/2.

4)  All the zeroes are -√3, √3 and -1/2.

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

x- 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

Problem 1 :

Find zero of the polynomial p(x) = x + 3.

Solution

Problem 2 :

Find the zeroes of quadratic polynomial x²-5x-6.

Solution

Problem 3 :

If 1 is a zero of the polynomial p(x) = ax2 - 3(a-1)x - 1, then find the value of 'a' ?            Solution

Problem 4 :

If the graph of a polynomial intersects the x – axis at only one point, can it be a quadratic polynomial?           Solution

Problem 5 :

What number should be added to the polynomial x2-5x+4, so that 3 is the zero of the polynomial?            Solution

Problem 6 :

If x – 3 and x – 1/3 are both factors of ax2 + 5x + b , show that a = b              Solution

Problem 7 :

If y = -1 is a zero of the polynomial q(y) = 4y3 + ky2 - y -1, then find the value of k

Solution

Problem 8 :

For what value of m is x3 – 2mx2 + 16 divisible by x + 2

Answer Key

1)  x = -3

2)  6 and -1

3)  a = 1

4)  Cannot

5)  2

6)  Proved

7)  k = 4

8)  m = 1

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