Let P(x)=x2+bx+c, where b and c are integers. If P(x) is a factor of both x4+6x2+25 and 3x4+4x2+28x+5, then
A
P(x)=0 has imaginary roots
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B
P(x)=0 has roots of opposite sign
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C
P(1)=4
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D
P(1)=6
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Solution
The correct option is CP(1)=4 Since P(x) divides both the expressions, hence P(x) also divides (3x4+4x2+28x+5)−3(x4+6x2+25) =−14x2+28x−70 =−14(x2−2x+5) which is a quadratic.
Hence, P(x)=x2−2x+5 ∴P(1)=4