Question

If roots of equation 3x2 + 5x + 1 = 0 are (secq1 - tanqı) and (cosecq2 - cotq2), then find the
equation whose roots are (secq1 + tanqı) and (cosecq2 + cotq2)​

Answer 1

Answer:

Step-by-step explanation:

equation 3x² + 5x + 1 = 0

secq1 - tanq1 = α

=> secq1 + tanq1  = 1/α

cosecq2 - cotq2 = β

=> cosecq2 + cotq2 = 1/β

In original equation sum of roots is α + β.

In new equation, the sum of roots is 1/α + 1/β.

This means x ----> 1/x

Thus 3x² + 5x + 1  ====> 3(1/x)² + 5(1/x) + 1 = 0

                             =====> 3/x² + 5/x + 1 = 0

                             =====> x² + 5x + 3 = 0