Value of a Polynomial f(x) at x = α –
The value of a polynomial f(x) at x = α is obtained by substituting x = α in the given polynomial and it is denoted by f(α).
Example.1) If f(x) = 3x³ + 2x² - 6x – 11, find f(3)
Ans.) We have f(x) = 3x³+ 2x²- 6x – 11
As per given condition, f(3) = {(3 X 3³) + (2 X 3²) – (6 X 3) – 11}
= {(3 X 27) + (2 X 9) – 18 – 11}
= {(81 + 18) – (18 + 11)}
= (99 – 29)
= 70 (Ans.)
Example.2) If f(x) = 5x³- 2x²+ 8x – 15, find f(- 2)
Ans.) We have f(x) = 5x³- 2x²+ 8x – 15
As per the given condition,
f(-2) = [{5 X (-2)³} – {2 X (-2)²} + {8 X (-2)} – 15]
= [{5 X (-8)} – (2 X 4) + (-16) – 15]
= (- 40 – 8 – 16 – 15)
= -79 (Ans.)
Example.3) If f(x) = 7x²- 3x + 8, find f(-1/2)
Ans.) We have f(x) = 7x²- 3x + 8
As per the given condition,
1 1 1
f(- -----) = [{7 X (- -----)²} – {3 X ( - -----)} + 8]
2 2 2
7 3
= ------- + ------- + 8
4 2
14 + 3
= ---------- + 8
4
17 + 32
= ----------
4
49
= ------- (Ans.)
4
Your second block of text...