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

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

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