Question

3. If f(x) = x4 – 4x3 + 3x² -2x+1; then
Prove that f(-2). f (1) + 65 f(0) = 0​

Answer 1

Answer:

f(x) = x⁴ - 4x³ + 3x² - 2x + 1

f(-2) = (-2)⁴ - 4(-2)³ + 3(-2)² - 2(-2) + 1

f(-2) = 16 - (4 × -8) + (3 × 4) - (2 × -2) + 1

f(-2) = 16 - (-32) + 12 - (-4) + 1

f(-2) = 16 + 32 + 12 + 4 + 1

f(-2) = 65

f(1) = 1⁴ - 4(1)³ + 3(1)² - 2(1) + 1

f(1) = 1 - (4 × 1) + (3 × 1) - (2 × 1) + 1

f(1) = 1 - 4 + 3 - 2 + 1

f(1) = -1

f(0) = 0⁴ - 4(0)³ + 3(0)² - 2(0) + 1

f(0) = 0 - (4 × 0) + (3 × 0) - (2 × 0) + 1

f(0) = 0 - 0 + 0 - 0 + 1

f(0) = 1

( f(-2) × f(1) ) + ( 65 × f(0) ) = 0

(65 × (-1) ) + (65 × 1) = 0

- 65 + 65 = 0

0 = 0