Q. 225.0( 4 Votes )

# If sin α and cos α are the roots of the equation ax^{2} + bx + c = 0, then b^{2} =

A. a^{2} – 2ac

B. a^{2} + 2ac

C. a^{2} – ac

D. a^{2} + ac

Answer :

Equation ax^{2} + bx + c = 0 has and as two roots

sin α + cos α =

sin α × cos α = c/a …eq(1)

…..eq (2)

But sin^{2} α + cos^{2} α = 1

∴ a^{2} (1 + 2 sinα.cos α) = b^{2}

Putting sin α × cos α = c/a, we get,

⇒ b^{2} = a^{2} + 2ac.

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