Question

If sin theta cos theta are the roots of x square + qx + r is is equal to zero then find the value q2-p2

Answer 1

Answer:

$\rm q^2-p^2=2pr$

Step-by-step explanation:

$\rm px^2 + qx +r=0$

$\rm ( \sin θ + \cos θ ) = \dfrac{q}{p}$

$\rm ( \sin θ + \cos θ )^2 = \dfrac{q^2}{p^2}$

$\rm 1+2 \bigg(\dfrac{r}{p} \bigg) = \dfrac{q^2}{p^2}$

$\rm \dfrac{p+2r}{p} = \dfrac{q^2}{p^2}$

$\rm p(p+2r)=q^2$

$\rm p^2+2pr=q^2$

$\rm 2pr=q^2-p^2$

$\rm q^2-p^2=2pr$