The quadratic equation 2x2 - 4x + 12 = 0 has
A. 2 distinct real roots
B. no real roots
C. 2 equal real roots
D. more than 2 real roots
Answer: The quadratic equation 2x2 - 4x + 12 = 0 has no real roots.
Let us check the nature of roots using the discriminant formula.
The nature of roots of the given equation can be given by,
D = b2 - 4ac = 0 for a quadratic equation ax2 + bx + c = 0
In the given quadratic equation 2x2 - 4x + 12 = 0, a = 2 b = -4 and c = 12
Substituting the values in D = b2 - 4ac we get,
D = (-4)² - (4)(2)(12) = 16 - 96 = -80 < 0
Since D is negative, it has no real roots.
Hence, option B i.e. no real root is the correct option.