Question

If sin  and cos  are the roots of the equation ax2

– bx + c = 0, then a, b and c satisfy the

relation​

Answer 1

Answer:

b²/a² = 1 + 2c/a is the relation

Explanation:

sum of roots is = b/a = sinx + cosx

product of roots = c/a = sinxcosx

b²/a² = sin²x + cos²x + 2sinxcosx = sin²x + cos²x + 2c/a

By rule of sine and cosine, sin²x + cos²x = 1 for x∈R

Therefor,

b²/a² = 1 + 2c/a

Answer 2

ANSWER

a²+b²+2ac=0

Explanation

-b²/a² = sin²x + cos²x + 2 sinx.cosx

c/a = sinx.cosx

-b²/a² = 1 + 2c/a     [∵sin²x +cos²x = 1]

move a² to RHS

-b² = a² + 2 c/a.a²

-b² = a² + 2ac

move -b² to RHS

∴ a² + b² + 2ac = 0