Question

2x²-6x+4<0 quadratic inequalities ​

Answer 1

Answer:

X < 1, X < 2

Step-by-step explanation:

2x²-6x+4<0

or 2(x²-3x+2)<0

or x²-3x+2<0

or x² - 2x - x + 2 < 0

or x(x - 2) -1(x - 2) < 0

or (x - 1)(x - 2) < 0

Answer 2

$\large\underline{\sf{Solution-}}$

The given quadratic inequality is

$\rm :\longmapsto\: {2x}^{2} - 6x + 4 < 0$

can be rewritten as

$\rm :\longmapsto\: 2({x}^{2} - 3x + 2 )< 0$

$\rm :\longmapsto\: {x}^{2} - 3x + 2 < 0$

$\rm :\longmapsto\: {x}^{2} - x - 2x + 2 < 0$

$\rm :\longmapsto\:x(x - 1) - 2(x - 1) < 0$

$\rm :\longmapsto\:(x - 1)(x - 2) < 0$

We know,

If a and b are two positive real numbers such that a < b, then

$\boxed{ \sf{ \: (x - a)(x - b) < 0 \: \implies \: a < x < b}}$

So, using this rule, we get

$\bf\implies \:1 < x < 2$

$\bf\implies \:x \: \in \: (1, \: 2)$

Hence,

The solution of

$\rm :\longmapsto\: {2x}^{2} - 6x + 4 < 0$

is

$\bf\implies \:x \: \in \: (1, \: 2)$