Mathematics
Find the value of k for the following quadratic equation, so that it has two equal roots.
kx(x - 2) + 6 = 0
Quadratic Equations
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Answer
Given,
Equation : kx(x - 2) + 6 = 0
⇒ kx2 - 2kx + 6 = 0
Comparing kx2 - 2kx + 6 = 0 with ax2 + bx + c = 0, we get :
a = k, b = -2k and c = 6.
For equal roots,
⇒ b2 - 4ac = 0
⇒ (-2k)2 - 4 × k × 6 = 0
⇒ 4k2 - 24k = 0
⇒ 4k(k - 6) = 0
⇒ 4k = 0 or k - 6 = 0
⇒ k = 0 or k = 6.
k cannot be equal to zero because then equation kx2 - 2kx + 6 = 0, will not be quadratic.
∴ k = 6.
Hence, k = 6.
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