#### Question

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

kx(x - 2) + 6 = 0

#### Solution

The given equation is

kx(x - 2) + 6 = 0

⇒ kx^{2} - 2kx + 6 = 0

The given equation is in the form of ax^{2} + bx + c = 0

where a = k, b = -2k and c = 6

Therefore, the discriminant

D = b^{2} - 4ac

= (-2k)^{2} - 4 x (k) x (6)

= 4k^{2} - 24k

= 4k(k - 6)

∵ Roots of the given equation are real and equal

∴ D = 0

⇒ 4k(k - 6) = 0

⇒ k = 0

Or

⇒ k - 6 = 0

⇒ k = 6

Hence, the value of k = 0, 6.

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#### APPEARS IN

Solution Find the Values Of K For Which the Roots Are Real and Equal in Each of the Following Equation: Kx(X - 2) + 6 = 0 Concept: Nature of Roots.