Q.28 If two roots of the equation \( \mathrm{x}^{3}-\mathrm{px}^{2}+\mathrm{q} \mathrm{x}-\mathrm{r}=0 \) are equal in magnitude but opposite in sign, then:
(1) \( \mathrm{pr}=\mathrm{q} \)
(2) \( \mathrm{qr}=\mathrm{p} \)
(3) \( \mathrm{pq}=\mathrm{r} \)
(4) none
Q.29 If \( \alpha, \beta \& \gamma \) are the roots of the equation \( x^{3}-x-1=0 \) then, \( \frac{1+\alpha}{1-\alpha}+\frac{1+\beta}{1-\beta}+\frac{1+\gamma}{1-\gamma} \) has the value equal to:
(1) zero
(2) \( -1 \)
(3) \( -7 \)
(4) 1
1. Q.30 For what value of \( \mathrm{a} \) and \( \mathrm{b} \) the equation \( \mathrm{x}^{4}-4 \mathrm{x}^{3}+\mathrm{ax}^{2}+ \) \( \mathrm{bx}+1=0 \) has four real positive roots?
(1) \( (-6,-4) \)
(2) \( (-6,5) \)
(3) \( (-6,4) \)
\( (4)(6,-4) \)
