Let p, q ∈ R. If 2 – √3 is a root of the quadratic equation,

1.	Let p, q ∈ R. If 2 – √3 is a root of the quadratic equation, x2 + px + q = 0, then :(1) p2 – 4q + 12 = 0(2) q2 – 4p – 16 = 0(3) q2 + 4p + 14 = 0(4) p2 – 4q – 12 = 0
Answer» Correct option (4) p² – 4q – 12 = 0 Explanation: If one root of equation x² + px + q = 0 is 2 – √3 then other root will be 2+ √3 ∴ equation x² – 4x + 1 = 0 ⇒ p = –4 and q = 1 ⇒ p² – 4q – 12 = 0

Let p, q ∈ R. If 2 – √3 is a root of the quadratic equation, x2 + px + q = 0, then :(1) p2 – 4q + 12 = 0(2) q2 – 4p – 16 = 0(3) q2 + 4p + 14 = 0(4) p2 – 4q – 12 = 0

Answer»

Correct option (4) p² – 4q – 12 = 0

Explanation:

If one root of equation x² + px + q = 0 is 2 – √3

then other root will be 2+ √3

∴ equation x² – 4x + 1 = 0

⇒ p = –4 and q = 1

⇒ p² – 4q – 12 = 0

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Let p, q ∈ R. If 2 – √3 is a root of the quadratic equation, x2 + px + q = 0, then :(1) p2 – 4q + 12 = 0(2) q2 – 4p – 16 = 0(3) q2 + 4p + 14 = 0(4) p2 – 4q – 12 = 0

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