(K + 1)X2 + 2(K + 3)X + (K + 8) = 0 - Mathematics

English0CBSEEnglish Medium Class 10Question PapersQuestion Papers1479Textbook Solutions33761MCQ Online Mock Tests19Important Solutions16432Concept Notes & Videos262Time Tables17SyllabusFind 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 - 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:

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

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SolutionShow 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.

shaalaa.comNature of Roots of a Quadratic Equation Report Error Is there an error in this question or solution?Q 2.11Q 2.1Q 2.12Chapter 4: Quadratic Equations - Exercise 4.6 [Page 41]

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RD Sharma Mathematics [English] Class 10Chapter 4 Quadratic EquationsExercise 4.6 | Q 2.11 | Page 41

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