On a number line a student marks where each linear divisor (x−a) is zero for the polynomial p(x)=x2−5x+6. The two values of a that give remainder 0 are the points marked. What is their sum?
Class 9Remainder TheoremPolynomials
A6
B10
C4
D5
Step-by-Step Solution
p(a)=0 when a2−5a+6=0, i.e. (a−2)(a−3)=0, so a=2 or a=3. Sum = 2 + 3 = 5.
Answer: D) 5
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