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Find the Values Of K For Which the Roots Are Real and Equal in Each of the Following Equation: (K + 1)X2 + 2(K + 3)X + (K + 8) = 0 - CBSE Class 10 - Mathematics

Question

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

(k + 1)x2 + 2(k + 3)x + (k + 8) = 0

Solution

The given quadric equation is (k + 1)x2 + 2(k + 3)x + (k + 8) = 0, and roots are real and equal

Then find the value of k.

Here,

a = (k + 1), b = 2(k + 3) and c = (k + 8)

As we know that D = b2 - 4ac

Putting the value of a = (k + 1), b = 2(k + 3) and c = (k + 8)

= (2(k + 3))2 - 4 x (k + 1) x (k + 8)

= (4k2 + 24k + 36) - 4(k2 + 9k + 8)

= 4k2 + 24k + 36 - 4k2 - 36k - 32

= -12k + 4

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

-12k + 4 = 0

12k = 4

k = 4/12

k = 1/3

Therefore, the value of k = 1/3.

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Solution Find the Values Of K For Which the Roots Are Real and Equal in Each of the Following Equation: (K + 1)X2 + 2(K + 3)X + (K + 8) = 0 Concept: Nature of Roots.
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