Calculate the discriminant and state how many real solutions each equation has:?

Question

1) 4x^2 - 6x + 4 = 0

2) 4x^2 - 4x + 1 = 0

Answer 1

The discriminant of ax^2 + bx + c = 0 is b^2-4*a*c
If +ve there are two real answers
if 0 there is one answer
if -ve there are two imaginary answers.

Answer 2

b^2-4ac = 0 => 2 actual equivalent roots b^2-4ac < 0 => 0 actual roots, 2 imaginary complicated conjugates b^2-4ac > 0 => 2 actual unequal roots b=-6 a=4 c=4 b^2=36 4ac=sixty 4 36-sixty 4 < 0 => 0 actual roots

Answer 3

1)
D = b² - 4ac
d = -6² - 4*4*4
d = 36 - 64 = a<0
There are no real roots.

2)
d = 4² - 4*4*1
d = 16 - 16
d = 0 ==> a=0
There are two real roots.

Answer 4

1). b²-4ac = 36-64 < 0, so no real solutions.
2). b²-4ac = 0, so there are 2 equal real solutions
(only 1 is also a correct answer.)