CBSE · Mathematics
Quadratic Equations
298 practice questions for CBSE — 126 easy · 156 medium · 16 hard. Every question is graded instantly with a step-by-step solution when you miss it.
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MCQ
If the roots of the equation $x^3-7 x^2+14 x-8=0$ are in geometric progression, then the difference between the largest and the smallest roots is
MCQ
$\operatorname{In} \frac{x^4-6 x^3+9 x^2+5 x-20}{x^2-x-2}=f(x)+\frac{a}{x+p}+\frac{b}{x+q}$ then $2(a+b)=$
MCQ
Let $f(x)=x^2+a x+b$, where $a, b \in R$. If $f(x)=0$ has all its roots imaginary, then the roots of $f(x)+f^{\prime}(x)+f^{\prime \prime}(x)=0$ are
MCQ
The harmonic mean of two numbers is $-\frac{8}{5}$ and their geometric mean is 2 . The quadratic equation whose roots are twice those numbers is
MCQ
If $(x-2)$ is a common factor of the expressions $x^2+a x+b$ and $x^2+c x+d$, then $\frac{b-d}{c-a}$ is equal to
MCQ
$\begin{aligned} & \text { If } \frac{x^3}{(2 x-1)(x-1)^2}=A+\frac{B}{2 x-1}+\frac{C}{x-1} \\ & +\frac{D}{(x-1)^2}, \text { then } 2 A-3 B+4 C+5 D=\end{aligned}$
MCQ
$\left{x\in\,\mathbb{R}:\frac{\sqrt{6+x-x^{2}}}{2x+5}\geq\,\frac{\sqrt{6+x-x^{2}}}{x+4}\right}=$
MCQ
Let $f(x)=(x-a)(x-b)-\left(\frac{a+b}{2}\right)$. If $f(x)=0$ has both non-negative roots, then the minimum value of $f(x)$.
MCQ
Match the following
MCQ
For real values of $x$ and $a$, if the expression $\frac{x+a}{2 x^2-3 x+1}$ assumes all real values, then
MCQ
What is the quotient of \(x^3-5 x^2+2 x+7\) when divided with \((x-1)\) ?
MCQ
$\alpha, \beta, \gamma$ are the roots of the equation $x^3-10 x^2+7 x+8=0$. Match the following and choose the correct answer.