Question

The roots of the equation x

2

+ px + q = 0 are tan 22° and tan 23 then​

Answer 1

Answer:

here is your answer

Step-by-step explanation:

all the best

tan(a+b)=(tana+tanb)/(1-tanatanb)

Answer 2

Given,

The roots of the equation x²+px+q are tan 22° and tan 23°.

To find,

We have to find the condition when tan 22° and tan 23° are the roots of the equation x²+px+q.

Solution,

p-q+1 = 0 is the true condition when tan 22° and tan 23° are the roots of the equation x²+px+q.

We can simply use the concept of the sum of roots and the product of roots to find the condition.

Given equation is x²+px+q

Sum of roots = -b/a

   tan 22° + tan 23° = -p                            (1)

Product of roots = c/a

   tan 22° * tan 23° = q                              (2)

Using the formula of tan(a+b), we get

tan(a+b) = tan a + tan b/ 1-tan a * tan b     (3)

Substituting the equation (1) and (2) in equation (3), we get

tan(22+23)° = tan 22° +tan 23°/ 1-tan 22° * tan 23°

 tan 45° =  -p/1-q                            (tan 45° =1)

          1 = -p/1-q

         1-q = -p

         p-q+1 = 0

which is the required condition to be find when tan 22° and tan 23° are the roots of the equation x²+px+q.

Hence, p-q+1 = 0 is the true condition when tan 22° and tan 23° are the roots of the equation x²+px+q.