Values Of A Polynomial Function
For a polynomial f(x) = 3x2 – 4x + 2. Values Of A Polynomial
To find its value at x = 3;
replace x by 3 everywhere.
So, the value of f(x) = 3x2 – 4x + 2 at x = 3 is
f(3) = 3 × 32 – 4 × 3 + 2
= 27 – 12 + 2 = 17.
Similarly, the value of polynomial
f(x) = 3x2 – 4x + 2,
(i) at x = –2 is f(–2) = 3(–2)2 –4(–2) + 2
= 12 + 8 + 2 = 22
(ii) at x = 0 is f(0) = 3(0)2 – 4(0) + 2
= 0 – 0 + 2 = 2
(iii) at x = \(\frac { 1 }{ 2 }\) is
\(f\left( \frac{1}{2} \right)=3{{\left( \frac{1}{2} \right)}^{2}}-4\left( \frac{1}{2} \right)+2\)
\(=\frac{3}{4}-2+2=\frac{3}{4}\)
Example 1: Find the value of the polynomial 5x – 4x2 + 3 at:
(i) x = 0 (ii) x = –1
Sol. Let p(x) = 5x – 4×2 + 3.
(i) At x = 0, p(0) = 5 × 0 – 4 × (0)2 + 3
= 0 – 0 + 3 = 3
(ii) At x = –1, p(–1) = 5(–1) – 4(–1)2 + 3
= –5 – 4 + 3 = – 6