Class 11Mathematics4-2.Quadratic Equations and InequationsSolution of quadratic equations and Nature of roots
DifficultIf $\alpha$ and $\beta$ $(\alpha < \beta)$ are the roots of the equation $(-2+\sqrt{3})(|\sqrt{x}-3|) + (x-6\sqrt{x}) + (9-2\sqrt{3}) = 0$, $x \ge 0$, then $\sqrt{\frac{\beta}{\alpha}} + \sqrt{\alpha\beta}$ is equal to:
- A$8$
- B$9$
- C$10$
- D$11$
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View SolutionWith respect to the roots of the equation $3x^3 + bx^2 + bx + 3 = 0$,match the items of List-$I$ with those of List-$II$.
List-$I$ List-$II$ $A$. All the roots are negative $I$. $(b - 3)^2 = 36 + P^2$ for $P \in R$ $B$. Two roots are complex $II$. $-3 < b < 9$ $C$. Two roots are positive $III$. $b \in (-\infty, -3) \cup (9, \infty)$ $D$. All roots are real and distinct $IV$. $b = 9$ $V$. $b = -3$
| List-$I$ | List-$II$ |
| $A$. All the roots are negative | $I$. $(b - 3)^2 = 36 + P^2$ for $P \in R$ |
| $B$. Two roots are complex | $II$. $-3 < b < 9$ |
| $C$. Two roots are positive | $III$. $b \in (-\infty, -3) \cup (9, \infty)$ |
| $D$. All roots are real and distinct | $IV$. $b = 9$ |
| $V$. $b = -3$ |
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