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Mathematics

Consider the following equation k2x2 - 2kx + 1 = 0

Assertion (A): This equation has real roots for all non-zero values of k.

Reason (R): The discriminant of this equation is zero.

  1. Assertion (A) is true, but Reason (R) is false.

  2. Assertion (A) is false, but Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Quadratic Equations

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Answer

Given,

Equation : k2x2 - 2kx + 1 = 0

Comparing above equation with ax2 + bx + c = 0, we get :

a = k2, b = -2k and c = 1

Discriminant (D) = b2 - 4ac

= (-2k)2 - 4 x k2 x 1

= 4k2 - 4k2

= 0.

So, reason (R) is true.

Since, D = 0 this means the equation has one repeated real root.

So, assertion (A) is true and reason (R) correctly explains assertion (A).

Thus, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

Hence, option 3 is the correct option.

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