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Find the Values of K for Which the Roots Are Real and Equal in Each of the Following Equation: (3k+1)X2 + 2(K + 1)X + K = 0 - CBSE Class 10 - Mathematics

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Question

Find the values of k for which the roots are real and equal in each of the following equation:

(3k+1)x2 + 2(k + 1)x + k = 0

Solution

The given quadric equation is (3k+1)x2 + 2(k + 1)x + k = 0, and roots are real and equal

Then find the value of k.

Here, a = (3k + 1), b = 2(k + 1) and c = k

As we know that D = b2 - 4ac

Putting the value of a = (3k + 1), b = 2(k + 1) and c = k

= (2(k + 1))2 - 4 x (3k + 1) x (k)

= 4(k2 + 2k + 1) - 4k(3k + 1)

= 4k2 + 8k + 4 - 12k2 - 4k

= -8k2 + 4k + 4

The given equation will have real and equal roots, if D = 0

Thus,

-8k2 + 4k + 4 = 0

-4(2k2 - k - 1) = 0

2k2 - k - 1 = 0

Now factorizing of the above equation

2k2 - k - 1 = 0

2k2 - 2k + k - 1 = 0

2k(k - 1) + 1(k - 1) = 0

(k - 1)(2k + 1) = 0

So, either

k - 1 = 0

k = 1

Or

2k + 1 = 0

2k = -1

k = -1/2

Therefore, the value of k = 1, -1/2

  Is there an error in this question or solution?

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Solution Find the Values of K for Which the Roots Are Real and Equal in Each of the Following Equation: (3k+1)X2 + 2(K + 1)X + K = 0 Concept: Nature of Roots.
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