Question

find the factor of the following.
$2x + 2x {}^{2} - 6x + 3$
​

Answer 1

$\huge\tt\underline\red{Ans}\underline {w}\underline\purple{er}\underline{:}\orange {}$

$\huge \underbrace \mathfrak \red{\bigstar Explanation}$

${ \bold { \purple{\underline{\large{Given : - }}}}} \:$

$2x + 2x {}^{2} - 6x + 3$

${ \bold { \purple{\underline{\large{Standard \: form : - }}}}} \:$

$2x {}^{2}+2x - 6x + 3$

$:⟹ 2x {}^{2}+2x - 6x + 3$

$:⟹ 2x {}^{2}-4x + 3$

$\tt \large { Dividing \: by \: 2 }$

$:⟹ \large{\frac{ 2x {}^{2}}{2}-\frac{4x}{2} + \frac{3}{2} }$

$:⟹ \large{\frac{ \cancel2x ^{2}}{\cancel2}-\frac{\cancel4x}{\cancel2} + \frac{3}{2} }$

$:⟹ x² -2x +\large{\frac{3}{2}}$

${ \bold { \purple{\underline{\huge{Solution : - }}}}} \:$

Let a = 1 , b = -2 , c = $\frac{3}{2}$

We know that,

$d= b²-4ac$

$:⟹ (-2)²-4×1×\frac{3}{2[}/tex] </p><p>[tex]:⟹ (-2)²-\cancel4×1×\frac{3}{\cancel2}$

$:⟹ 4 -2 ×1×3$

$:⟹ 4- 6$

$:⟹ -2$

$\tt \therefore -2 <0$

We know that,

If d < 0 then the equation have no roots

[tex] \\ [/tex]

Therefore the equation have no factors

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