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If an angle A of a Δ A B C satisfies 5 cos A + 3 = 0 , then the roots of the quadratic equation 9 x 2 + 27 x + 20 = 0 are

Options

  1. Asec A ,   cot A
  2. Bsec A ,   tan A
  3. Ctan A ,   cos A
  4. Dsin A ,   sec A

Correct answer

B. sec A ,   tan A

Step-by-step solution

We have, 5 cos A + 3 = 0 ⇒ cos A = - 3 5 Clearly, A ∈ 90 ° , 180 ° Now, roots of equation 9 x 2 + 27 x + 20 = 0 ⇒ x = - 27 ± 729 - 720 18 = - 27 ± 3 18 ⇒ x = - 5 3 ,   - 4 3 Then, - 5 3 = sec A and - 4 3 = tan A . Hence, the roots are sec A and tan A .

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