Question

Hello! here is my tutorial on quadratic equation:)

Answer 1

consider the quadratic equation\[ax^2+bx+c=0 \space a \neq 0\]dividing both sides by 'a'. we get \[x^2+\frac{b}{a}x+\frac{c}{a}=0\]\[x^2+\frac{2b}{2a}x+\left( \frac{b}{2a} \right)^2-\left( \frac{b}{2a} \right)^2+\frac{c}{a}=0\]\[\left( x+\frac{b}{2a} \right)^2-\left( \frac{b}{2a} \right)^2+\frac{c}{a}=0\]\[\left( x+\frac{b}{2a} \right)^2=\left( \frac{b}{2a} \right)^2-\frac{c}{a}\]\[x+\frac{b}{2a}={\sqrt{b^2-4ac}\over4a^2}\]\[x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\] \[b^2-4ac=D \space is \space called \space discriminant.\]

Answer 2

typo i think it's 4a, not 4a^2 :D Nice job tho.

Answer 3

a) If D>0 then there are two distinct roots given\[\alpha={-b + \sqrt{b^2-4ac}\over2a}\]\[\beta={-b-\sqrt{b^2-4ac}\over2a}\]b) if D=0 then the roots are equal & real\[\alpha+\beta={-b \over a}\]c) if D<0 then there are no real roots
sum of the roots alpha+beta=-b/a
&
the product of the roots alpha*beta=c/a
Therefore the quadratic equation is\[x^2-(\alpha+\beta)x+(\alpha \beta)=0\]

Answer 4

im interested to know which part of the quadratic equation tells you if a polynomial is factorable. @jiteshmeghwal9

Answer 5

sir ! i think it's the middle term.

Answer 6

Have an Example in ur tutorial @jiteshmeghwal9 ;)

Answer 7

nyss

Answer 8

sorry i meant quadratic formula not equation

Answer 9

\[\Huge{\color{gold}{\star \star}{\color{blue}{Keep \space It \space Up \space Brother}}}\]

Answer 10

@lgbasallote sir. am i right??

Answer 11

How should i know? I was asking you o.O

Answer 12

Lol no. Ive seen so many questions about it but idk the answer so i was hoping you did since you were making a tutorial heh. Im not as sadistic as tou think :p

Answer 13

Btw you did not answer my question...i was asking which part of the quadratic FORMULA states whether a quadratic equation is factorable :(

Answer 14

What do you mean?

Answer 15

sir the discriminant tells whether the given equation is factorable

Answer 16

& i have given the tutorial of solving a quadratic equation

Answer 17

\[b^2-4ac=d \space is \space called \space "DISCRIMINANT"\]

Answer 18

@lgbasallote sir!

Answer 19

good job!!

Answer 20

thanx!

Answer 21

i see thanks

Answer 22

yw:)

Answer 23

if d is a perfect square, then the equation is factorable.