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State whether the following quadratic equations have two distinct real roots or not. Justify your answer $2 x 2 − 39 x + 19 = 0$

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No, the quadratic equation does not have two distinct real roots.

Yes, the quadratic equation does have two distinct real roots.

Both 1 and 2

None of these

answer is A.

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Detailed Solution

Given is a quadratic equation,

2 x 2 − 39 x + 19 = 0

.
We have to find whether the quadratic equation has two distinct real roots or not.
Compare the given equation with general equation

a x 2 + b x + c = 0

, we get

a = 2, b = − 39, c = 19

By substituting the values the discriminant for the given equation is,

D = b 2 − 4 a c D = − 39 2 − 4 × 2 × 19 D = 99 − 423 D = 1 − 423

Thus,

D = − v e

Therefore, the roots are not real.

D < 0

, No, the quadratic equation does not have two distinct real roots.
Therefore, the correct option is 1.

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