Question

solve x^2+1/4x+3/12=0​

Answer 1

Given -

• $\sf{\dfrac{x^2 + 1}{4x} + \dfrac{3}{12} = 0}$

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Solution -

We can write the given equation as

• $\sf{\dfrac{x^2 + 1}{4x} + \dfrac{1}{4} = 0}$

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Cross multiplying

$\tt\dashrightarrow{\dfrac{4(x^2 + 1) + 4x}{4x \times 4} = 0}$

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$\tt\dashrightarrow{\dfrac{4x^2 + 4 + 4x}{16x} = 0}$

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$\tt\dashrightarrow{4x^2 + 4x + 4 = 0}$

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Taking 4 as common from the whole equation

$\tt\dashrightarrow{4(x^2 + x + 1) = 0}$

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$\tt\dashrightarrow{x^2 + x + 1 = 0}$

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By middle term spiliting

$\tt\dashrightarrow{x^2 + x + x + 1 = 0}$

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$\tt\dashrightarrow{x(x + 1) + 1(x + 1) = 0}$

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$\tt\dashrightarrow{(x + 1) (x + 1) = 0}$

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Calculating zeroes of the equation

$\begin{lgathered}\begin{array}{c|c}\sf x + 1 = 0&\sf x + 1 = 0\\\\\bf x = -1&\bf x = -1\end{array}\end{lgathered}$

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Hence,

• Value of x is -1.

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Answer 2

$4x^{2}+x+1$ no real solution because D<0

see the pic that i have attached