Question

If the roots of the quadratic equation x² + px + q = 0 are tan 300 and tan 150, respectively then the value of 2+q-p is

(a) 2

(b) 3

(c) 0

(d) 1

 

 

Answer 1

Given that x² + px + q = 0

Sum of roots = tan 300 + tan 150 = -p

Product of roots = tan 300 tan 150 = q

We know tan (a+b) = (tan a + tan b)/(1- tan a tan b)

tan 450 = tan (30 + 15)0

1 = (tan 300 + tan 150)/(1 – tan 300tan 150)

1 = -p/(1-q)

=> 1-q = -p

q-p = 1

2+q-p = 2+1

= 3

 

Hence option b is the answer.

 

 

Value of 2+p-q is 3