Question

Condition that sinx,cosxmAy be roots of ax^2+bx+c=0

Answer 1

Answer:

a = 1, b = -(sinX + cosX), $c = (sinX)(cosX)$

Step-by-step explanation:

If sinX and cosX are the roots of $ax^{2} + bx + c =0$, then (x - sinX)(x - cosX) = $ax^{2} + bx + c =0$

$(x - sinX)(x - cosX) = ax^{2} + bx + c \\x^{2} - xsinX - xcosX + (sinX)(cosX) = ax^{2} + bx + c \\x^{2} - x(sinX+cosX) + (sinX)(cosX) = ax^{2} + bx + c \\ x^{2} - (sinX + cosX)x + (sinX)(cosX) = ax^{2} + bx + c$

By comparing, we have

$ax^{2} = x^{2}$

∴ a = 1

$bx = - (sinX + cosX)x$

∴ b = -(sinX + cosX)

$c = (sinX)(cosX)$

Hope this helped!

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