find the zeroes of the polynomial and verify it 4x²+4x+1
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Step-by-step explanation:
We have,
4x² - 4x + 1 = 0 [ Given ]
⇒4x² - 2x - 2x + 1 = 0
⇒ 2x ( 2x - 1 ) - 1 ( 2x - 1 ) = 0
⇒ ( 2x - 1 ) ( 2x - 1 ) = 0
⇒ 2x - 1 = 0 and 2x - 1 = 0
⇒ x = 1/2 and x = 1/2
Therefore, the zeroes of 4x² - 4x + 1 are 1/2 and 1/2.
★ Sum of the zeroes :
1/2 + 1/2 = - coefficient of x / coefficient of x²
⇒ 1 + 1 / 2 = - ( - 4 ) / 4
⇒ 2/2 = 4/4
⇒ 1 = 1
★ Product of the zeroes :
1/2 × 1/2 = constant term / coefficient of x²
⇒ 1/4 = 1/4
Hope it helps you
Eva*
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