Question

19. Show that 1 is not a zero of the polynomial 4x4- 3x3+ 2x2 – 5x + 1.​

Answer 1

Answer:

let p(x) = 4x^4 - 3x³ + 2x² - 5x + 1

p(1) = 4×1^4 - 3×1³ + 2×1² - 5×1 + 1 = -1

since p(1) is not equal to 0

hence p(1) is not a zero of p(x)

Answer 2

       $\underline{\bold{Solution:}}$

       $\text{Let }p(x) = 4x^{4} - 3x^{3} + 2x^{2} - 5x + 1 = 0$

       $\text{We must show that 1 is not a zero of }p(x)$

       $\text{We know that, A number is the zero of the polynomial if L.H.S = R.H.S of}\\\text{the equation}$

$\implies \text{If }p(1) = 0\text{ then 1 is a zero of }p(x)$

$\implies \boxed{p(1) = 4(1)^{4} - 3(1)^{3} + 2(1)^{2} - 5(1) + 1 = 0 }$

$\implies \boxed{p(1) = 4(1) - 3(1)+ 2(1) - 5(1) + 1 = 0 }$

$\implies \boxed{p(1) = 4 - 3+ 2 - 5 + 1 = 0 }$

$\implies \boxed{p(1) = 7-8 = 0 }$

$\implies \boxed{p(1) = -1 \neq 0 }$

$\implies \text{L.H.S}\neq \text{R.H.S}$

  $\therefore \text{ }\text{ 1 is not a zero of }p(x) = 4x^{4} - 3x^{3} + 2x^{2} - 5x + 1 = 0$