If sin theta and cos theta are the roots of t | vedclass

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(B) Given that $\sin 	heta$ and $\cos 	heta$ are the roots of the quadratic equation $ax^2 - bx + c = 0$. From the properties of roots, the sum of r

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$a^2 - b^2 + 2ac = 0$

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(B) Given that $\sin 	heta$ and $\cos 	heta$ are the roots of the quadratic equation $ax^2 - bx + c = 0$. From the properties of roots, the sum of roots is $\sin 	heta + \cos 	heta = \frac{b}{a}$ and the product of roots is $\sin 	heta \cdot \cos 	heta = \frac{c}{a}$. Squaring the sum of roots, we get $(\sin 	heta + \cos 	heta)^2 = (\frac{b}{a})^2$. $\sin^2 	heta + \cos^2 	heta + 2 \sin 	heta \cos 	heta = \frac{b^2}{a^2}$. Since $\sin^2 	heta + \cos^2 	heta = 1$, we have $1 + 2(\frac{c}{a}) = \frac{b^2}{a^2}$. Multiplying by $a^2$, we get $a^2 + 2ac = b^2$. Rearranging the terms, we obtain $a^2 - b^2 + 2ac = 0$.

If $\sin \theta$ and $\cos \theta$ are the roots of the equation $ax^2 - bx + c = 0$, then $a, b$ and $c$ satisfy the relation:

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