If `sin alpha and cos alpha` are roots of the equation `px^2 + qx+r=0` then :

Options

A. `p^(2) +q^(2) -2pr =0`
B. `(p+r)^(2) =q^(2) +r^(2)`
C. `p^(2)-q^(2) + 2pr=0`
D. `(p+r)^(2)=q^(2) -r^(2)`

Answer

C

Explanation

Since , `sin prop and cos prop ` are the roots of the equation
` px^(2) +qx =r=0`
` sin prop + cos prop = - q/p`
` and p sin^(2) prop + q sin prop +r =0`
` p cos^(2) prop + q cos prop + r =0`
Adding Eqs (i) and (ii) we get
` p (sin^(2) prop + cos^(2) prop) +q (sin prop + cos prop) +2r=0`
` Rightarrow p + q (-q/p) + 2r =0`
` Rightarrow p^(2) -q^(2) +2rp =0`