Question

Show that 1 is a zero of the polynomial 4x^4-3x^3+2x^2-5x+1

Answer 1

Note:

★ If x = a is a zero of the polynomial p(x) , then the polynomial becomes zero at x = a , ie ; p(a) = 0 .

★ If the polynomial p(x) becomes zero at x = a , then x = a is said to be its zero .

Solution:

Let the given polynomial be p(x) .

Thus,

p(x) = 4x⁴ - 2x³ + 2x² - 5x + 1 .

Nkw,

Now putting x = 1 in the given polynomial p(x) ,

We have ;

=> p(x) = 4x⁴ - 2x³ + 2x² - 5x + 1

=> p(1) = 4•1⁴ - 2•1³ + 2•1² - 5•1 + 1

=> p(1) = 4 - 2 + 2 - 5 + 1

=> p(1) = 0

Since p(1) = 0 , thus x = 1 is zero of the given polynomial .

Hence proved .