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# Find the Values Of K For Which the Roots Are Real and Equal in Each of the Following Equation: K2x2 - 2(2k - 1)X + 4 = 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:

k2x2 - 2(2k - 1)x + 4 = 0

#### Solution

The given equation is k2x2 - 2(2k - 1)x + 4 = 0

The given equation is in the form of ax2 + bx + c = 0

where a = k2, b = -2(2k - 1) and c = 4

therefore, the discriminant

D = b2 - 4ac

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

= 4(2k - 1)2 - 16k2

= 4(4k2 + 1 - 4k) - 16k2

= 16k2 + 4 - 16k - 16k2

= 4 - 16k

∵ Roots of the given equation are real and equal

∴ D = 0

⇒ 4 - 16k = 0

⇒ -16k = -4

rARrk=(-4)/-16

⇒ k = 1/4

Hence, the value of K = 1/4

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Solution Find the Values Of K For Which the Roots Are Real and Equal in Each of the Following Equation: K2x2 - 2(2k - 1)X + 4 = 0 Concept: Nature of Roots.
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