for which Value of A and B are the zeros of q(x) = x²+2x²+a also the zeros of the polynomial p(x) = x5 -x⁴-4x3+2x2+3x+b ? with zeros of p(x) are not the zeros of q(x) ?
request you please answer my question fast it is urgent
Answers
Answered by
8
p(x) = x5 – x4 – 4x3 + 3x2 + 3x + b
q(x) = x3 + 2x2 + a
Zeroes of q(x) are also the zeroes of p(x)
Þ q(x) is a factor of p(x)
To find the another factor of p(x), it should be divided by q(x).

x2 - 3x + 2 = (x – 2)(x – 1)
Therefore, 2 and 1 are the other zeroes of p(x).
Similarly, when p(x) is divided by x2 - 3x + 2, the quotient is x3 + 2x2 – 1 and the
Remainder is (b + 2).
x3 + 2x2 – 1 = x3 + 2x2 + a
⇒ a = -1
Remainder = 0
⇒ (b + 2) = 0
⇒ b = -2
Hence, the values of 'a' and 'b' are -1 and -2 respectively
q(x) = x3 + 2x2 + a
Zeroes of q(x) are also the zeroes of p(x)
Þ q(x) is a factor of p(x)
To find the another factor of p(x), it should be divided by q(x).

x2 - 3x + 2 = (x – 2)(x – 1)
Therefore, 2 and 1 are the other zeroes of p(x).
Similarly, when p(x) is divided by x2 - 3x + 2, the quotient is x3 + 2x2 – 1 and the
Remainder is (b + 2).
x3 + 2x2 – 1 = x3 + 2x2 + a
⇒ a = -1
Remainder = 0
⇒ (b + 2) = 0
⇒ b = -2
Hence, the values of 'a' and 'b' are -1 and -2 respectively
Similar questions