Class 11Mathematics2 Complex Numbers and Quadratic Equations: Quadratic EquationsSolution of quadratic equations and Nature of roots
EasyThe roots of the equation $|x^2-x-6|=x+2$ are
- A$-2, 1, 4$
- B$0, 2, 4$
- C$0, 1, 4$
- D$-2, 2, 4$
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DifficultJEE MAIN 2023
View SolutionLet $\alpha$ and $\beta$ be the roots of the quadratic equation $a x^2+b x+c=0$. Observe the lists given below:
List-$I$ List-$II$ $(i)$ $\alpha = \beta$ $(A)$ $(ac^2)^{1/3} + (a^2c)^{1/3} + b = 0$ $(ii)$ $\alpha = 2\beta$ $(B)$ $2b^2 = 9ac$ $(iii)$ $\alpha = 3\beta$ $(C)$ $b^2 = 6ac$ $(iv)$ $\alpha = \beta^2$ $(D)$ $3b^2 = 16ac$ $(E)$ $b^2 = 4ac$ $(F)$ $(ac^2)^{1/3} + (a^2c)^{1/3} = b$
The correct match of List-$I$ from List-$II$ is:
| List-$I$ | List-$II$ |
| $(i)$ $\alpha = \beta$ | $(A)$ $(ac^2)^{1/3} + (a^2c)^{1/3} + b = 0$ |
| $(ii)$ $\alpha = 2\beta$ | $(B)$ $2b^2 = 9ac$ |
| $(iii)$ $\alpha = 3\beta$ | $(C)$ $b^2 = 6ac$ |
| $(iv)$ $\alpha = \beta^2$ | $(D)$ $3b^2 = 16ac$ |
| $(E)$ $b^2 = 4ac$ | |
| $(F)$ $(ac^2)^{1/3} + (a^2c)^{1/3} = b$ |
The correct match of List-$I$ from List-$II$ is:
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