Question

If sin α and cos α are the roots of the equation ax² + bx + c = 0, then b² =
A. a² – 2ac
B. a² + 2ac
C. a² – ac
D. a² + ac

Answer 1

B. a² + 2ac

Step-by-step explanation:

ax² + bx + c = 0

sin α and cos α are roots of the equation.

Sum of roots = sin α + cos α = -b/a

Product of roots = sin α. cos α = c/a  

(sin α + cos α)² = sin²α + cos²α + 2sinα.cosα

(-b/a)² = 1 + 2c/a

 b² = a²  (1 + 2c/a)

 b² =  a(a +2c)

b² =  a² +2ac

Option B is the answer.