Q. 24.2( 225 Votes )
For what values of k, the roots of equation x2 + 4x + k = 0 are real?
Or
Find the value of k for which the roots of equation 3x2 – 10x + k = 0 are reciprocal of each other?
Answer :
For roots to be real D ≥ 0
⇒ b2 - 4ac ≥ 0
For x2 + 4x + k = 0,
⇒16 – 4k ≥ 0
⇒ – 4k ≥ - 16⇒4k ≤ 16
⇒k ≤ 4
Or
Consider 3x2 – 10x + k = 0,
Compare the given equation with the general equation ax2 + bx + c = 0
So, a = 3, b = -10, c = k
Let, the roots of the equation be x and 1/x.
Product of the roots 
⇒ k = 3
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(x2 + 1)2 - x2 = 0 has
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