If `sin theta and cos theta` are the roots of `ax^(2)+bx+ c=0`, then constants a, b,c will satisfy which one of the following conditions?

Options

A. `a^(2) + b^(2) + 2ac + =0`
B. ` a^(2) + b^(2) - 2ac =0`
C. ` a^(2) - b^(2) + 2ac =0`
D. `-a^(2)+ b^(2) + 2ac =0`

Answer

C

Explanation

As given `sin theta and cos theta` are the roots of the equation `ax^(2) + bx + c = 0.`
So, sum of roots `= sin theta + cos theta = -b/a " "` …(1) and product of roots `= sin theta cos theta = c/a " "` …(2)
On squaring both both sides in Eq. (1), we get
`(sin theta + cos theta )^(2) = b^(2)/a^(2) `
`rArr sin^(2) theta + cos^(2) theta + 2sin theta cos theta = b^(2)/a^(2) `
`rArr 1+ (2c)/a = b^(2)/a^(2) " " `
`rArr a^(2) + 2ca = b^(2)`
` a^(2) - b^(2) + 2ac = 0 `