Prove that 4 and 1 are the zeros of the quadratic polynomial p(x) = x² — 5x + 4. Also verify the relationship between the zeros and the coefficients of p(x).

Here p(x) = x² – 5x + 4

To prove that 4 and 1 are the zeros of p(x), we need to prove that p(4) = p(1) = 0.

p(4) = (4)² – 5(4) + 4

= 16 – 20 + 4

= 0

p(1) = (1)² – 5(1) + 4

= 1– 5 + 4

= 0

Hence proved that 4 and 1 are the zeros of the quadratic polynomial p(x) = x² – 5x + 4.

In p(x) = x² – 5x + 4

a = 1, b = –5, c = 4

Sum of zeros = 4 + 1 = 5

= – (–5)

= – = – = –

Product of zeros = 4×1 = 4

= = =

Hence verified the relationship between the zeros and the coefficients of p(x).