Question

what factoring technique did you use to come up with the of each quadratic equation?? Explain how you use this technique ​

Answer 1

$\huge\mathbb\red{ANSWER}$

I use direct method for factorisaton

let's see it by an example

ie 2x² + 4x + 3 = 0

we have to convert it into x² + bx + c = 0 form or we have to remove coefficient of x² ie 2

to this we divide whole equation by 2

$\frac{ 2 {x}^{2} + 4x +3}{2}$

${x}^{2} + 2x + \frac{3}{2}$

now we take avrage of b ie 2

$\green {avrage \: of \:any \: number: = \frac{any \: number \: }{2} }$

so avrage of 2 is 2 / 2 = 1

then substract any number u from 1 ie [ 1 - u]

also add any number u in 1 ie [1 + u]

therefore multiply both of them

(1 + u )(1 - u) = 1² - u² ------(1) [tex]\yellow{by\:using\:a²-b²\:property}[/tex]

then

$\blue { {1}^{2} - {u}^{2} = \frac{3}{2} }$

by solving it

$1 - {u}^{2} = \frac{3}{2} \\ \\ - {u}^{2} = \frac{3}{2} - 1 \\ \\ - {u}^{2} = \frac{3 - 2}{2} \\ \\ - {u}^{2} = \frac{1}{2} \\ \\ u = \sqrt{ \frac{1}{2} }$

now put value of u in equation 1

$1 - \sqrt{ \frac{1}{2} } \: \: and \: 1 + \sqrt{ \frac{1}{2} } \\ \\ 1 - \frac{1}{ \sqrt{2} } \: \: and \: 1 + \frac{1}{ \sqrt{2} } \\ \\ \frac{ \sqrt{2} - 1 }{ \sqrt{2} } \: and \: \: \frac{ \sqrt{2 } + 1}{ \sqrt{2} }$

then

vaule of x

$(x - \frac{ \sqrt{2} + 1 }{2} )(x + \frac{ \sqrt{2} - 1 }{2} )$

hope it helps you

be brainly