Question

find the zeroes of the polynomial and find the relation between the zeroes and the coefficient.

4x^2-4x+1

Answer 1

Answer:

4x² - 4x + 1

Splitting it's middle term-

4x² - 2x - 2x + 1

2x ( 2x - 1) - 1 ( 2x - 1 )

(2x - 1) ( 2x - 1 ) = 0

By zero product rule -

x = 1/2 and x = 1/2

Verification;

sum of zeroes = -b/a

⇒ 1/2 + 1/2 = - (-4)/4

⇒ 2/2 = 4/4

⇒ 1 = 1

Verified!

Product of zeroes = c/a

⇒ 1/2 * 1/2 = 1/4

⇒ 1/4 = 1/4

Verified!

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Thanks for the question!