If `sin theta` and `cos theta` are the roots of the quadratic equation `px^2 + qx + r = 0 (p != 0),` then which of the following relation holds good?A. `q^(2)-p^(2)=2pr`B. `p^(2)-q^(2)=2pr`C. `p^(2)+q^(2)+2pr=0`D. `(p-q)^(2)=2pr`

If `sin theta` and `cos theta` are the roots of the quadratic equation

1.	If `sin theta` and `cos theta` are the roots of the quadratic equation `px^2 + qx + r = 0 (p != 0),` then which of the following relation holds good?A. `q^(2)-p^(2)=2pr`B. `p^(2)-q^(2)=2pr`C. `p^(2)+q^(2)+2pr=0`D. `(p-q)^(2)=2pr`
Answer» Correct Answer - A (i) For the equation `ax^(2)+bx+c=0`,the sum of roots is `(-b)/(a)`, and product of the roots is `( c)/(a)`. (ii) Sum of the roots, `sin theta+ cos theta =(-q)/(p)`. (iii) Product of the roots ` sin theta * cos theta =(r )/(p)`. (iv) Eliminate `theta`, by using the formula `(a+b)^(2)=a^(2)+b^(2)+2ab` from the above equations.