JEE MAINS PRACTICE · Mathematics
Quadratic Equations
418 practice questions for JEE Mains Practice — 147 easy · 240 medium · 31 hard. Every question is graded instantly with a step-by-step solution when you miss it.
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MCQ
Let $a, b, c$ be real numbers with $a \neq 0$ and let $\alpha, \beta$ be the roots of the equation $a x^2+b x+c=0$, then $a^3 x^2+a b c x+c^3=0$ has roots
MCQ
If $a=\cos \frac{2 \pi}{7}+i \sin \frac{2 \pi}{7}$, then the quadratic equation whose roots are $\alpha=a+a^2+a^4$ and $\beta=a^3+a^5+a^6$, is
MCQ
The number of real solutions of the equation $1+\left|e^x-1\right|=e^x\left(e^x-2\right)$ is
MCQ
If $\alpha, \beta$ are the roots of $x^2-3 x+1=0$, then the equation whose roots are $\frac{1}{\alpha-2}, \frac{1}{\beta-2}$, is
MCQ
If the roots of the equation $(a-1)\left(x^2+x+1\right)^2$ $=(a+1)\left(x^4+x^2+1\right)$ are real and distinct then the value of $a \in$
MCQ
If $x^2+p x+q=0$ is the quadratic equation whose roots are $a-2$ and $b-2$, where $a$ and $b$ are the roots of $x^2-3 x+1=0$, then
MCQ
If the equation $x^2+p x+q=0$ and $x^2+q x+p=0$ have a common root then $p+q+1$ is equal to
MCQ
If $a, b, c$ are three distinct positive real numbers of real roots of $a x^2+2 b|x|-c=0$ is
MCQ
The sum of the real solutions of equation $2|x|^2+51=|1+20 x|$ is
MCQ
The quadratic equation whose roots are $\frac{1}{3+\sqrt{2}}$ and $\frac{1}{3-\sqrt{2}}$, will be
MCQ
If the roots of the equation $\frac{\alpha}{x-\alpha}+\frac{\beta}{x-\beta}=1$ be equal in magnitude but opposite in sign, then $\alpha+\beta$ is equal to
MCQ
If the roots of the equation $x^2-2 a x+a^2+a-3=0$ are real and less than 3 , then