If sin- and cos- are the roots of the equations a x2-b x-c-0- then b2-a a2-2 a cb a2-2 a cc a2-a cd a2-a c

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Standard XII

Mathematics

General Solution of sin theta = sin alpha

If sinα and c...

Question

If sin α and cos α are the roots of the equations ax²+ bx + c = 0, then b² =

(a) a² − 2ac
(b) a² + 2ac
(c) a² − ac
(d) a² + ac

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Solution

The given quadric equation is , and are roots of given equation.

And,

Then, as we know that sum of the roots

…. (1)

And the product of the roots

…. (2)

Squaring both sides of equation (1) we get

Putting the value of , we get

Putting the value of , we get

Therefore, the value of

Thus, the correct answer is

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If sin α and cos α are the roots of the equations ax2 + bx + c = 0, then b2 = (a) a2 − 2ac (b) a2 + 2ac (c) a2 − ac (d) a2 + ac

If sin α and cos α are the roots of the equations ax²+ bx + c = 0, then b² =

(a) a² − 2ac
(b) a² + 2ac
(c) a² − ac
(d) a² + ac