JEE MAINS PRACTICE · Mathematics
Quadratic Equation
574 practice questions for JEE Mains Practice — 222 easy · 225 medium · 127 hard. Every question is graded instantly with a step-by-step solution when you miss it.
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MCQ
If the roots $x^2+a x+9=0$ are complex, then
MCQ
If $\alpha$ and $\beta$ are the roots of $4 x^2+3 x+7=0$, then the value of $\frac{1}{\alpha}+\frac{1}{\beta}$ is
MCQ
The quadratic equation whose roots are $\frac{1}{3+\sqrt{2}}$ and $\frac{1}{3-\sqrt{2}}$, will be
MCQ
If $b \lt 0$, then the roots $x_1$ and $x_2$ of the equation $2 x^2+6 x+b=0$, satisfy the condition $\left(\frac{x_1}{x_2}\right)+\left(\frac{x_2}{x_1}\right) \lt K$, where $K$ is equal to
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
The value of $a(a \geq b)$ for which the sum of the cubes of the roots of $x^2-(a-2) x+(a-3)=0$ assumes the least value, is
MCQ
If $a\gt1$, roots of the equation $(1-a) x^2+3 a x-1=0$ are
MCQ
If $f(x)=x^2+2 b x+2 c^2$ and $g(x)=-x^2-2 c x+b^2$ are such that $\min f(x) \gt \max g(x)$, then relation between $b$ and $c$ is
MCQ
If the roots of the equation $x^2-2 a x+a^2+a-3=0$ are real and less than 3 , then
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
The condition that one root of the equation $a x^2+b x+c=0$ may be square of the other, is
MCQ
The equation $(\cos p-1) x^2+\cos p x$ $+\sin p=0$ in the variable $x$, has real roots. Then, $p$ can take any value in the interval