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AP TET Paper 2 Math and Science Model Paper 2

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Question : 106 of 150

Marks: +1, -0

For what value of

k

3x^{2} - 2x + k = 0

have equal roots?

$-3$
$1/3$
3
$-1/3$

Solution:

Concept:

A quadratic equation

ax^2 + bx + c = 0

has equal roots when its discriminant is zero:

D = b^2 - 4ac = 0

.

Explanation:

Given equation:

3x^2 - 2x + k = 0

.

Compare with the standard form:

a = 3

,

b = -2

,

c = k

.

For equal roots, the discriminant must be zero:

D = 0

.

So,

b^2 - 4ac = 0

.

Substitute the values:

(-2)^2 - 4(3)(k) = 0

.

This gives:

4 - 12k = 0

.

Thus,

12k = 4

.

Therefore,

k = \frac{4}{12} = \frac{1}{3}

.

Answer:

k = \frac{1}{3}

, which corresponds to option B.

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