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# The quadratic equation 2x^{2} - 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 2x^{2} - 4x + 12 = 0 has no real roots.

Let us check the nature of roots using the discriminant formula.

**Explanation:**

The nature of roots of the given equation can be given by,

D = b^{2} - 4ac = 0 for a quadratic equation ax^{2} + bx + c = 0

In the given quadratic equation 2x^{2} - 4x + 12 = 0, a = 2 b = -4 and c = 12

Substituting the values in D = b^{2} - 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.

Q1: The quadratic equations 2x² - 4x + 12 is equal to 0 has

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