First slide

Theory of equations

Question

If $\sin α$ and $\cos α$ are roots of the equation $p x^{2} + q x + r = 0$ then ,

Moderate

A

$p^{2} - q^{2} + 2 p r = 0$
B

$(p + r)^{2} = q^{2} - r^{2}$
C

$p^{2} + q^{2} - 2 p r = 0$
D

$(p - r)^{2} = q^{2} + r^{2}$

Solution

We have,
$\sin α + \cos α = - \frac{q}{p}$ and $\sin α \cos α = \frac{r}{p}$
$\Rightarrow (\sin α + \cos α)^{2} = \frac{q^{2}}{p^{2}}$ and $\sin α \cos α = \frac{r}{p}$
$\Rightarrow 1 + 2 \sin α \cos α = \frac{q^{2}}{p^{2}}$ and $\sin α \cos α = \frac{r}{p}$
$\Rightarrow 1 + \frac{2 r}{p} = \frac{q^{2}}{p^{2}} \Rightarrow p^{2} - q^{2} + 2 p r = 0$

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