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Find all the quadratic factors of x^8 + ...

Find all the quadratic factors of `x^8 + x^4 + 1` with real coefficients.

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Let P(x) be a quadratic polynomial with real coefficients such that for all real x the relation 2(1+P(x))=P(x-1)+P(x+1) holds. If P(0)=8 and P(2)=32, then Sum of all the coefficients of P(x) is:

Let P(x) be quadratic polynomical with real coefficient such tht for all real x the relation 2(1 + P(x)) = P(x - 1) + P(x + 1) holds. If P(0) = 8 and P(2) = 32 then Sum of all coefficients of P(x) can not be

Let P(x) be quadratic polynomical with real coefficient such tht for all real x the relation 2(1 + P(x)) = P(x - 1) + P(x + 1) holds. If P(0) = 8 and P(2) = 32 then Sum of all coefficients of P(x) can not be

Let Q(x) be a quadratic polynomial with real coefficients such that for all real x the relation, 2(1+Q(x)) =Q(x - 1) +Q(x +1) holds good. If Q(0) = 8 and Q(2) = 32 then The number of integral values of 'x' for which Q(x) gives negative real values.