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
Problem 2 :
n = 3; -4 and i are zeros; f(-3) = 60
Problem 3 :
n = 4; 3, 1/3, and 1 + 2i are zeros; f(1) = 48
Problem 4 :
n = 3; -1 and -3 + 2i are zeros; leading coefficient is 1
Problem 5 :
n = 4; 2i, 5, and -5 are zeros; leading coefficient is 1.
1) f(x) = -5x^{3} + 15x^{2} - 5x + 15
2) f(x) = 6x^{3} + 24x^{2} + 6x + 24
3) f(x) = -9x^{4}+48x^{3}-114x^{2}+168x-45
4) f(x) = x^{3} + 7x^{2} + 19x + 13
5) x^{4} - 21x^{2} - 100
Problem 1 :
Find all the zeroes of the polynomial x^{3} + 3x^{2} – 2x – 6, if two of its zeroes are -√2 and √2.
Problem 2 :
Find all the zeroes of the polynomial 2x^{3} + x^{2} – 6x – 3, if two of its zeroes are -√3 and √3.
Problem 3 :
Obtain all other zeroes of the polynomial 2x^{3} - 4x – x^{2} + 2, if two of its zeroes are √2 and -√2.
Problem 4 :
If the polynomial 6x^{4} + 8x^{3} + 17x^{2} + 21x + 7 is divided by another polynomial 3x^{2} + 4x + 1 then the remainder comes out to be ax + b, find ‘a’ and ‘b’.
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) = ax^{2} - 3(a - 1)x - 1
then find the value of 'a' and find other zero.?
Problem 2 :
What number should be added to the polynomial
x^{2 }- 5x + 4
so that 3 is the zero of the polynomial?
Problem 3 :
If one of the zeros of the cubic polynomial
x^{3} + ax^{2} + bx + c is -1
then what will be the product of the other two zeros?
Problem 4 :
Obtain all other zeros of the polynomial
2x^{4} - 9x^{3}+ 5x^{2} + 3x - 1
if two of its zeros are 2 - √3 and 2 + √3?
Problem 5 :
Find the zeros of the polynomial
f(x) = x^{3} - 5x^{2} -2x +24
if it is given that the product of its two zeros is 12?
Problem 6 :
If the zeros of the polynomial f(x) = x^{3} – 3x^{2} - 6x + 8 are of the form a-b, a, a+b, then find all the zeros.
Problem 7 :
If α, β are the two zeros of the polynomial
f(y) = y^{2} - 8y + a and α^{2} + β^{2} = 40
find the value of ‘a’?
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
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM