Quant · Algebra

Linear and Quadratic Equations

4 sub-topics · 35 lessons · 69 questions · 14 PYQs

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Linear Equations9 lessons · 18 questions · 2 PYQs

Quadratic Equations13 lessons · 31 questions · 7 PYQs

Higher-Degree Equations7 lessons · 10 questions · 3 PYQs

Exponential Equations6 lessons · 10 questions · 2 PYQs

Formula sheet

Celsius-Fahrenheit conversion
$F=1.8C+32,\qquad C=\dfrac{F-32}{1.8}$
Factoring out the common power
$a^{x+m}+a^{x+n}=a^{x}\left(a^{m}+a^{n}\right)$
Equal powers of the same base
$a^{f(x)}=a^{g(x)}\ (a>0,\ a\neq1)\ \Rightarrow\ f(x)=g(x)$
Quadratic in a power
$p\,a^{2x}+q\,a^{x}+r=0:\ \text{put } t=a^{x}>0$
Swapped-coefficient pair
$ax+by=c,\ bx+ay=d\ \Rightarrow\ x+y=\dfrac{c+d}{a+b},\ x-y=\dfrac{c-d}{a-b}$
Sum of squares of the roots
$\alpha^{2}+\beta^{2}+\gamma^{2}=\left(\sum\alpha\right)^{2}-2\sum\alpha\beta$
Vieta's relations for a cubic
$ax^{3}+bx^{2}+cx+d=0:\quad \sum\alpha=-\dfrac{b}{a},\ \sum\alpha\beta=\dfrac{c}{a},\ \alpha\beta\gamma=-\dfrac{d}{a}$
Quadratic formula and Vieta's relations
$ax^{2}+bx+c=0:\quad x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a},\qquad \alpha+\beta=-\dfrac{b}{a},\ \alpha\beta=\dfrac{c}{a}$