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 +…

If an angle A of a ΔABC satisfies 5cosA+3=0, then the roots of the quadratic equation 9x2+27x+20=0 are
  1. secA, cotA
  2. secA, tanA
  3. tanA, cosA
  4. sinA, secA

Solution

We have,

5cosA+3=0⇒cosA=-35

Clearly, A∈90°,180°

Now, roots of equation

9x2+27x+20=0 

⇒x=-27±729-72018=-27±318

⇒x=-53, -43

Then, -53=secA and -43=tanA.

Hence, the roots are secA and tanA.

Asked in: JEE Main 2018 (16 Apr Online)

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