Question

Formulas and tips for quadratic equations

Answer 1

standard quadratic equation
$a {x}^{2} + bx + c = 0$
let $\alpha \: \: and \: \beta$ are zeros of quadratic polynomial.
sum of zeros
$\alpha + \beta = \frac{ - b}{a} \\ \alpha \beta = \frac{c}{a}$
these are the basic formulas .
if product and sum are given then polynomial is calculated as
${x}^{2} - ( - \frac{b}{a} )x + \frac{c}{a} = 0$

nature of roots depends upon Discriminate D
$D = {b}^{2} - 4ac \\if \: D = 0 \\ roots \: are \: real \: and \: equal \: \frac{ - b}{2a}$
if D>0, roots are real and unequal
$\frac{ - b \: + - \sqrt{D} }{2a}$
if D <0,roots are not real.
SridharAcharya formula or quadratic formula
$\frac{ - b + - \sqrt{D} }{2a}$