Consider the polynomial .

MATHEMATICS · Multi-part · AoPS · Mathematics · Quadratic Equations - Part 1 · Quadratic Equations - Part 1

Problem

Consider the polynomial

p(x)=3x^2-5x+2

. (i) Calculate

p(x)

for each

x

\{-2,-1,0,1,2\}

and complete the following table.

x

\; : \;

-2

-1

0

1

2

p(x)

: \; _____ \; _____ \; _____ \; _____ \; _____ (ii) From your results in part (i), identify all integer values of

x

among the given set for which

p(x)=0

. Explain your choice briefly. (iii) Verify the value(s) you obtained in part (ii) by direct substitution in

p(x)

. State your conclusion clearly.