Problem 1 :
If y = 1 is a zero of the polynomial
q(y) = 4y^{3} + ky^{2} - y - 1
then find the value of k.
Problem 2 :
For what value of m is x^{3} - 2mx^{2} + 16 is divisible by x + 2.
Problem 3 :
The polynomials x^{3} + 2x^{2} - 5ax - 7 and x^{3} + ax^{2} - 12x + 6 when divided by x + 1 and x - 2 respectively, leave remainders R_{1} and R_{2} respectively. Find the value of a in each of the following cases :
i) R_{1} = R_{2}
ii) R_{1} + R_{2} = 0
iii) 2R_{1} + R_{2} = 0
Problem 4 :
When a polynomial
p(x) = x^{4} - 2x^{3} + 3x^{2} - ax + b
is divisible by x - 1 and x + 1, the remainders are 5 and 19 respectively. Find the remainder when p(x) is divided by x - 2.
Problem 5 :
If x - 3 and x - 1/3 are both factors of ax^{2} + 5x + b, show that a = b.
1) k = -2
2) m = 1
3) i) When R_{1} = R_{2} ==> a = -4
ii) R_{1} + R_{2} = 0 ==> a = 16/9
iii) 2R_{1} + R_{2} = 0 ==> a = 11/7
4) Values of a and b are 5 and 8 respectively.
p(2) = 10
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM