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Answers
given polynomial :-
4x² - 4x + 1
we can find zeroes of a quadratic polynomial by two methods. one is splitting the middle term and the other one is quadratic formula.
quadratic formula is basically a lengthy process. splitting method is easy and short but sometimes we have to use the quadratic formula.
by splitting the middle term,
➡ 4x² - 4x + 1 = 0
➡ 4x² - (2x + 2x) + 1 = 0
➡ 4x² - 2x - 2x + 1 = 0
➡ 2x(2x - 1) - 1(2x - 1) = 0
➡ (2x - 1) (2x - 1) = 0
➡ x = 1/2, 1/2
by quadratic formula,
D = b² - 4ac
= (-4)² - 4(4)(1)
= 16 - 16
= 0
one more thing, D or discriminate tells us the nature of the quadratic equation.
if D is positive, then it have two real and distinct roots. if D is 0, then it have two real and equal roots and if D is negative, then it has no real roots.
here D is 0, hence it has two real roots.
now x = (-b ± √D)/2a
➡ x = (4 ± √0)/8
➡ x = 4/8, 4/8
➡ x = 1/2
the correct answer is 1/2
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