The discriminant of the equation is a value that helps to determine the nature of the roots of a quadratic equation.
Solve the discriminant of the equation.
To solve the value under the square root sign in the quadratic formula.
Class X maths EXERCISE 4.4 Questions No:2 Part (ii)
Find the values of k for each of the following quadratic equations, so that they have two equal roots. kx (x – 2) + 6 = 0
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kx (x – 2) + 6 = 0
On simplification, we get kx² – 2kx + 6 = 0
For the quadratic equation kx² – 2kx + 6 = 0 we have a = k, b = – 2k, c = 6.
Therefore,
b² – 4ac = (-2k)² – 4 × k × 6 = 4k² – 24k
For equal roots, we have 4k² – 24k = 0
⇒ 4k (k – 6) = 0
⇒ 4k = 0 or (k – 6) = 0
⇒ k = 0 or k = 6
But k ≠ 0, as it doesn’t satisfies the equation kx(x -2) + 6 = 0.
Hence, k = 6