If (p(x)=5x+a) and (q(x)=2x-9), what is (a) if the zero of (p(x)+q(x)) is (2)?

Correct answer: -5

First add the polynomials: \(p(x)+q(x)=5x+a+2x-9=7x+a-9\). Since \(2\) is a zero of this polynomial, substitute \(x=2\): \(7(2)+a-9=0\). Thus, \(14+a-9=0\), so \(a+5=0\) and \(a=-5\). If \(a=-3\), the polynomial does not give zero at \(x=2\). Exam tip: when a zero is given, substitute that value in the polynomial and equate the result to \(0\).