Let `alpha and beta (a lt beta) " be the roots of the equation " x^(2) + bx + c = 0," where " b gt 0 and c lt 0 . `
Consider the following :
1. `alpha + beta + alpha beta gt 0`
2. `alpha^(2) beta + beta ^(2) alpha gt 0 `
Which of the above is//are correct ?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Answer

B

Explanation

Sum of roots `= alpha + beta = - b `
Multiplication of roots `= alpha beta = c `
Hence
` alpha + beta + alpha beta = - b + c " "alpha^(2) beta+ beta^(2) = alpha beta(alpha + beta) = -bc`
` :. b gt 0 & c gt0`
` :. -b + c lt 0 & -bc gt 0 `