If p(x) =x2+bx+c, where b, c ∈ I Ifp (x) is a factor of both x4+6x2+25 and 3x4+4x2+28x+5, then P(2) equals

Question

If p(x) =x2+bx+c, where b, c ∈ I Ifp (x) is a factor of both x4+6x2+25 and 3x4+4x2+28x+5, then P(2) equals (A) 0 (B) 5 (C) 4 (D) 2

Tardigrade Admin · Accepted Answer

p(x) is a factor of x4+6x2+25=g (x) (say) and 3x4+4x2+28x+5 = h (x) (say) then p(x) must be the factor of h (x) -k g (x) ∀ x ∈ R ∴ =(3x4+4x2+28x+5)-3(x4+6x2+25) =-14(x2-2x+5) ∴ p(x) = x2-2x+5 ∴ p(2) =4-4+5=5

Q. If $p (x) = x^{2} + b x + c$ , where $b, c \in I$ Ifp (x) is a factor of both $x^{4} + 6 x^{2} + 25$ and $3 x^{4} + 4 x^{2} + 28 x + 5$ , then $P (2)$ equals

$0$

$5$

$4$

$2$

Q. If p(x)=x2+bx+c, where b,c∈I Ifp (x) is a factor of both x4+6x2+25 and 3x4+4x2+28x+5, then P(2) equals

0

5

4

2

p(x) is a factor of x4+6x2+25=g(x) (say) and 3x4+4x2+28x+5=h(x) (say) then p(x) must be the factor of h(x)−kg(x)∀x∈R ∴=(3x4+4x2+28x+5)−3(x4+6x2+25) =−14(x2−2x+5) ∴p(x)=x2−2x+5 ∴p(2)=4−4+5=5

Q. If $p (x) = x^{2} + b x + c$ , where $b, c \in I$ Ifp (x) is a factor of both $x^{4} + 6 x^{2} + 25$ and $3 x^{4} + 4 x^{2} + 28 x + 5$ , then $P (2)$ equals

$0$

$5$

$4$

$2$