According to the Fundamental Theorem of Algebra, 4x^2 + 11x - 20 = 0 has two solutions. How many of those solutions

are integers?

1 answer

According to the fundamental theorem of Algebra, a polynomial equation of degree n has exactly n complex solutions (including repeated solutions).

Therefore, the equation 4x^2 + 11x - 20 = 0 has exactly 2 solutions.

To determine if any of these solutions are integers, we can try to factor the equation or use the quadratic formula.

Factoring the equation:
4x^2 + 11x - 20 = 0
(4x - 5)(x + 4) = 0

Setting each factor equal to 0:
4x - 5 = 0 or x + 4 = 0
4x = 5 or x = -4
x = 5/4 or x = -4

So the equation has two solutions, x = 5/4 and x = -4.

Of these two solutions, only one of them is an integer (x = -4). Therefore, there is only 1 integer solution to the equation 4x^2 + 11x - 20 = 0.