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The roots of Ax^2+Bx+1 are the same as the roots of x^2 - 3x + 5 + 4x^2 - x - 4. What is A+B?
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The hidden meaning of the " given " part in this problem is that
the set of all complex roots of one polynomial is the same
as the set of all complex roots of the other polynomial.
Reduce the long polynomial to the standard form of a quadratic polynomial by combining
like terms. You will get 5x^2 - 4x + 1.
Thus this shortened polynomial has the same roots as the polynomial Ax^2 + Bx + 1.
The fact that two polynomials of the same degree with real coefficients have the same roots
means that these polynomials have proportional coefficients
(one common proportionality factor for two sets of coefficients).
But these polynomials have one common value "1" of the constant terms.
It implies that co-named coefficients in these polynomials are equal:
A = 5, B = -4.
So, A + B = 5 + (-4) = 1. ANSWER
Solved.
