Complex Numbers And Quadratic Equations

Question
CBSEENMA11015600

If the roots of the quadratic equation x2 + px + q = 0 are tan30° and tan15°, respectively then the value of 2 + q − p is

  • 2

  • 3

  • 0

  • 1

Solution

B.

3

x2 + px + q = 0
tan 30° + tan 15° = − p
tan 30° ⋅ tan 15° = q
tan space 45 to the power of straight o space equals space fraction numerator tan space 30 to the power of straight o space plus space tan space 15 to the power of straight o over denominator 1 minus tan space 30 to the power of straight o space tan space 15 to the power of straight o end fraction space
equals space fraction numerator negative straight p over denominator 1 minus straight q end fraction space equals 1
⇒ − p = 1 − q
⇒ q − p = 1
∴ 2 + q − p = 3

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