Question

discriminat 4x²-2x+2=0​

Answer 1

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❏ Discriminant of 4x² - 2x + 2 = 0

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❏ Discriminant of a quadratic equations is a formula to check whether quadratic equation has real or imaginary roots.

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❏ It is represent by capital "D"

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Formula of Discriminant :

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$\boxed{ \bold { \red { :\leadsto \; Discriminant = D = b^{2} - 4ac }} }$

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❏ Equation =  4x² - 2x + 2 = 0

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Let's Start !

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Here,

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a = coefficient of x² = 4

b = coefficient of x = (-2)

c = constant term = 2

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Now let's substitute following values in our formula !

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$\boxed{ \bold { \red { :\leadsto \; Discriminant = D = b^{2} - 4ac }} }$

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$\bold { \blue { :\implies \; D = (-2)^{2} - 4\times(4)\times(2) }}$

$\bold { \orange { :\implies \; D = (-2)^{2} - (4 \times 4 \times 2) }}$

$\bold { \orange { :\implies \; D = 4 - (16 \times 2) }}$

$\bold { \blue { :\implies \; D = 4 - (32) }}$

$\bold { \orange { :\implies \; D =( -28) }}$

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$\boxed { \bold { \therefore Value \; Discriminant = D =( -28) }}$

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Explore more about Discriminant :

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Here is a simple chart to identify type of root according to given equation by using the concept of discriminant .-.

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$\boxed {\bold { Value \; of \;Discriminant \; D =\begin {cases}D > 0 & \implies Roots \; are \; real \; and \; distinct \\ D = 0 & \implies Roots \; are \; real \; and \; equal \\ D < 0 & \implies Roots \; are \; imaginary \\ \end {cases} } }$

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Hope this helps u.../

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