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
Problem 1 :
Find zero of the polynomial p(x) = x + 3.
Problem 2 :
Find the zeroes of quadratic polynomial x²-5x-6.
Problem 3 :
If 1 is a zero of the polynomial p(x) = ax^{2} - 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 x^{2}-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 ax^{2} + 5x + b , show that a = b Solution
Problem 7 :
If y = -1 is a zero of the polynomial q(y) = 4y^{3} + ky^{2} - y -1, then find the value of k
Problem 8 :
For what value of m is x^{3} – 2mx^{2} + 16 divisible by x + 2
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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Mar 14, 24 10:12 AM
Mar 14, 24 09:52 AM