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Mathematics

Assertion (A): The roots of the quadratic equation 3x2 + 7x + 8 = 0 are imaginary.

Reason (R): The discriminant of a quadratic equation is always positive.

  1. Both A and R are true, and R is the correct explanation of A.

  2. Both A and R are true, but R is not the correct explanation of A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Quadratic Equations

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Answer

Given,

⇒ 3x2 + 7x + 8 = 0

Comparing 3x2 + 7x + 8 = 0 with ax2 + bx + c = 0 we get,

a = 3, b = 7 and c = 8.

We know that,

Discriminant (D) = b2 - 4ac

= (7)2 - 4 × (3) × (8)

= 49 - 96 = -47; which is negative.

Therefore, the equation has imaginary and unequal roots.

So, Assertion (A) is true.

The Discriminant of quadratic equation can be positive, negative or equal to zero.

So, Reason (R) is false.

A is true, R is false.

Hence, option 3 is the correct option.

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