Quantitative Aptitude

Algebra

3,715 Questions

All Polynomial Roots and Coefficients 2451 Zero-Product Root Finding 667 Linear System Manipulation 162 Polynomial Theorems and Reduction 85 Algebraic Identity Simplification 82 Surds and Indices 70 Modulus and Absolute Value 54 Algebraic Expression Substitution 46 Algebraic Fraction Simplification 33 Logarithmic Equations 25 Repeated Series Sum 12 Linear Equation Word Problems 9

Algebra Questions

Multiple choice

Let a, $\beta $ are the roots of the equation ${ x }^{ 2 }-2x+3=0$ then the equation whose roots are $P={ 3a }^{ 2 }+5a-2$ and $Q={ \beta }^{ 3 }{ -\beta }^{ 2 }+\beta +5$ is _______________.

${ x }^{ 2 }+3x+2=0$
${ x }^{ 2 }-3x+2=0$
${ x }^{ 2 }-3x-2=0$
$-{ x }^{ 2 }-3x+9=0$

Reveal answer Fill a bubble to check yourself

Multiple choice

The difference between the corresponding roots of the equations $\displaystyle x^{2} + ax + b = 0$ and $\displaystyle x^{2} + bx + a = 0$ is same, then

$\displaystyle a+b-4 = 0$
$\displaystyle a-b+4 = 0$
$\displaystyle a+b+4 = 0$
None of these

Reveal answer Fill a bubble to check yourself

Multiple choice

The sum of the roots of the quadratic equation $ax^2+bx+c=0$ are ________________.

$\dfrac{b}{a}$
$\dfrac{c}{a}$
$-\dfrac{b}{a}$
None of these

Reveal answer Fill a bubble to check yourself

Multiple choice

Let $\alpha$ and $\beta$ be the roots of equation $px^2+qx+r=0.p \neq 0.$ If p,q and r in AP and $\cfrac 1 \alpha +\cfrac 1 \beta =4,$ then the value of $|\alpha - \beta|$ is

$\cfrac {\sqrt {61}}{9}$
$\cfrac {2\sqrt 17}{9}$
$\cfrac {\sqrt {34}}{9}$
$\cfrac {2\sqrt 13}{9}$

Reveal answer Fill a bubble to check yourself

Multiple choice

All the values of $m$ for which both roots of the equation $\displaystyle x^{2}+2mx+m^{2}-1=0 $ are greater than $-2$ but less than $4$ lie in the interval

$\displaystyle -2< m< 0 $
$\displaystyle m> 3 $
$\displaystyle -1< m< 3 $
$\displaystyle 1< m< 4 $

Reveal answer Fill a bubble to check yourself

Multiple choice

If the difference between the roots of the equation $\displaystyle x^{2}+ax+1=0 $ is less than $\displaystyle \sqrt{5} $, then the set of possible values of $a$ is

$\displaystyle (3,\infty) $
$\displaystyle (-\infty ,-3) $
$(-3,3)$
$\displaystyle (-3,\infty) $

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Multiple choice

The ratio of the roots of the equation $\displaystyle a_{1}x^{2} + b_{1}x + c_{1} = 0$ and $\displaystyle a_{2}x^{2} + b_{2}x + c_{2} = 0$ are equal , then

$\displaystyle \left ( \frac{b_{1}}{b_{2}} \right )^{2} = \frac{a_{2} c_{2}}{a_{1} c_{1}}$
$\displaystyle \left ( \frac{c_{1}}{c_{2}} \right )^{2} = \frac{b_{1} c_{2}}{c_{1} b_{2}}$
$\displaystyle \left ( \frac{a_{1}}{a_{2}} \right )^{2} = \left ( \frac{c_{1}}{c_{2}} \right )^{2}$
$\displaystyle \left ( \frac{b_{1}}{b_{2}} \right )^{2} = \frac{a_{1} c_{1}}{a_{2} c_{2}}$

Reveal answer Fill a bubble to check yourself

Multiple choice

If the roots of the equation $\displaystyle x^{2}-bx+c=0 $ be two consecutive integers, then $\displaystyle b^{2}-4c $ equals

$3$
$-2$
$1$
$2$

Reveal answer Fill a bubble to check yourself

Multiple choice

If one root of the equation $\displaystyle x^{2}+px+12=0 $ is $4$ while the equation $\displaystyle x^{2}+px+q=0$ has equal roots, then one value of $q$ is

$3$
$12$
$\displaystyle \frac{49}{4}$
$4$

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Multiple choice

If one of the zeroes of the quadratic polynomial $(k-1)x^{2}+kx+1$ is $-3$, then the value of $k$ is.

$\dfrac{4}{3}$
$\dfrac{-4}{3}$
$\dfrac{2}{3}$
$\dfrac{-2}{3}$

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Multiple choice

The number of irrational roots of the equation $4x/(x^2+x+3)+5x/(x^2-5x+3)=-3/2$ is?

$4$
$0$
$1$
$2$

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Multiple choice

The roots of the equation $t^3+3at^2+3bt+c=0$ are $z_1, z_2, z_3$ which represent the vertices of an equilateral triangle, then?

$a^2=3b$
$b^2=a$
$a^2=b$
$b^2=3a$

Reveal answer Fill a bubble to check yourself

Multiple choice

Solving the following quadratic equations by factorization method: $ 6x^{2}-17ix-12 = 0 $

$ \dfrac{3}{2}i,\dfrac{4}{3}i $
$ 2i, 3i$
$ -\dfrac{3}{2}i,\dfrac{4}{3}i $
$ 3i, 4i $

Reveal answer Fill a bubble to check yourself

Multiple choice

If both $p$ and $q$ belongs to the set $(1,2,3,4)$, then how many equations of the form $px^2+qx+1=0$ will have real roots ?

$12$
$10$
$7$
$6$

Reveal answer Fill a bubble to check yourself

Multiple choice

If $a,b$, where $a>b$, are the roots of the quadratic equation $x^{2}+3x-4=0$, then the value of $5a+b$ is

$1$
$-2$
$-3$
none of these

Reveal answer Fill a bubble to check yourself

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