exam Maths Puzzle Numerical Ability

how can one determine if a word problem can be solved using the Quadratic Equation and why one can determine that?
Thank you so much!!

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exam Other Question

The length of the longer base of a trapezoid is 18 meters, and the length of the median is 15 meters. Find the length of the shorter base of the trapezoid. How many positive real solutions are there in:

f(x) = -2x^4 + 3x^3 + 7x^2 + 2

a. 0
b. 2
c. 1
d. None, there is no x-term