Question

write the condition if roots of x square + bx + c = 20 or sin theta and Cos theta​

Answer 1

x²+ bx+ c-20=0 is the given equation

If roots of this equation is sin(a) and cos(a) respectively.

★ Then sum of roots = sin(a)+cos(a)= –b.......................….......( 1 )

★ And product of roots = sin(a)*cos(a) = c–20........................( 2 )

★ We know , sin²(a)+cos²(a) =1

★ Then on squaring equation (1) we get

★ sin²(a)+cos²(a)+2sin(a)cos(a) = b²

Substituting equation (2) and applying the above mentioned identity

We get :-

b²–2c+39=0