If `sin alpha and cos alpha` are the roots of the equation `px^(2) +qx+r=0,` then which one of the following is correct ?

Options

A. ` p^(2) + q^(2) - 2pr = 0 `
B. ` p^(2) - q^(2) + 2pr = 0 `
C. `(p+r)^(2) = 2(p^(2)+r^(2))`
D. None of these

Answer

B

Explanation

`sin alpha and cos alpha` are the roots of the equation
` px^(2) + qx + r = 0 `
` :. sin alpha + cos alpha = -q/p" "`…(i)
` and sin alpha cos alpha = r/p " "`…(ii)
From equation (i)
` (sin alpha + cos alpha ) ^(2) = q^(2)/p^(2)`
`rArr sin ^(2) alpha + cos^(2) alpha + 2 sin alpha cos alpha = q^(2)/p^(2)`
`rArr 1+2. r/p = q^(2)/p^(2)`
`rArr p^(2) - q^(2) + 2pr = 0 `