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Question
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.
Options
0 only
4
8 only
0, 8
Solution
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is 0, 8.
Explanation:
Given equation is 2x2 – kx + k = 0
On comparing with ax2 + bx + c = 0, we get
a = 2, b = –k and c = k
For equal roots, the discriminant must be zero
i.e., D = b2 – 4ac = 0
⇒ (–k)2 – 4(2)k = 0
⇒ k2 – 8k = 0
⇒ k(k – 8) = 0
∴ k = 0, 8
Hence, the required values of k are 0 and 8.
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