Class 11Mathematics2 Complex Numbers and Quadratic Equations: Quadratic EquationsSolution of quadratic equations and Nature of roots
DifficultThe sum of all the solutions of the equation $(8)^{2x} - 16 \cdot (8)^x + 48 = 0$ is:
- A$1 + \log_6(8)$
- B$\log_8(6)$
- C$1 + \log_8(6)$
- D$\log_8(4)$
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The number of ordered pairs $(a, b)$ of integers such that $1 \leq a, b \leq 2021$ and the equations $x^2 - ax + b = 0$ and $x^3 - ax^2 + bx + a - b = 0$ have a common real root is
If the roots of the equation $qx^2 + px + q = 0$,where $p$ and $q$ are real,are complex,then the roots of the equation $x^2 - 4qx + p^2 = 0$ are
Medium
View SolutionIf $mn=3$ and $\frac{1}{m}+\frac{1}{n}=\frac{4}{3}$,then the value of $0.1+0.1^{\frac{1}{m}}+0.1^{\frac{1}{n}}$ is
If $f(x)$ is a second degree polynomial such that $f(x) \geq 0$ for all $x \in R$,$f(-3) = 0$,and $f(0) = 18$,then find $f(3)$.
The number of real roots of the equation $\sqrt{x^2-4x+3}+\sqrt{x^2-9}=\sqrt{4x^2-14x+6}$ is:
DifficultJEE MAIN 2023
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