FIND NTH DEGREE POLYNOMIAL FUNCTION WITH GIVEN CONDITION WORKSHEET

Find an nth degree polynomial function with real coefficients satisfying the given conditions.

Problem 1 :

n = 3; 3 and i are zeros; f(2) = 25

Solution

Problem 2 :

n = 3; -4 and i are zeros; f(-3) = 60

Solution

Problem 3 :

n = 4; 3, 1/3, and 1 + 2i are zeros; f(1) = 48

Solution

Problem 4 :

n = 3; -1 and -3 + 2i are zeros; leading coefficient is 1

Solution

Problem 5 :

n = 4; 2i, 5, and -5 are zeros; leading coefficient is 1.

Solution

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