Question

The question below has two statements, I and Impark your answer as
For on equation ax³ + bx² + cx + d = 0, if its roots are α, β and y, then
Ι. \( \alpha \)+ \(\beta\)+ \(\gamma \) = c/a 
ΙI. \(\alpha\beta\gamma\) = d

• A. Statement I is True, but not the other one.
• B. Statement II is True, but not the other one.
• C. Both the statements are True.
• D. Neither of the statements is True.

Answer 1

The Correct Option is B

\(a x^3 + b x^2 + c x + d = 0\), if its roots are \(\alpha, \beta, \gamma\)
According to question,
\(\alpha + \beta + \gamma = \begin{bmatrix} -b \\ a \end{bmatrix}\) for Statement I.
\((\alpha\times \beta) + (\beta \times \gamma) + (\gamma \times \alpha) = \frac{a}{c}\)
\(\alpha\ \beta\ \gamma= \frac{- d}{a}\) for Statement II.
Both the statements are not True.
The correct option is (B)