Question

find the zeros of the quadratic polynomial 4x2 - 4x +1 is : A. 2
B. 3
C. 4

Answer 1

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