Q2 of 39 Page 1

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?

For roots to be real D ≥ 0

⇒ b2 - 4ac ≥ 0
For x2 + 4x + k = 0, 

⇒ 42 - 4(1)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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