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Question
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
Options
0
4
0 and 4
0 or 4
Solution
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is 0 or 4.
Explanation:
Given quadratic equation be,
kx2 + kx + 1 = 0
On comparing with ax2 + bx + c = 0
We have, a = k; b = k; c = 1
Here D = b2 – 4ac
= k2 – 4k
Since given equation has equal roots
∴ D = 0
`\implies` k2 – 4k = 0
`\implies` k(k – 4) = 0
`\implies` k = 0 or 4
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Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
