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Alex73 [517]
3 years ago
6

What would be the root of (x^2 + 2)?

Mathematics
1 answer:
Vladimir [108]3 years ago
5 0

Answer:

The roots of the equation are \sqrt{2}i and  -\sqrt{2}i

Step-by-step explanation:

The roots of a quadratic equation y = ax² + bx + c are the values of x at y = 0

∵ y = x² + 2

- To find the roots of it equate y by 0

∴ 0 = x² + 2

- Switch the two sides

∴ x² + 2 = 0

- Subtract 2 from both sides

∴ x² = -2

- Take √  for both sides

∴ x = ± \sqrt{-2}

- There is no square root for negative numbers

∴ There is no real roots for this equation but there are imaginary roots

∵ \sqrt{-1}=i

∴ \sqrt{-2}=\sqrt{2}*\sqrt{-1}

- Substitute \sqrt{-1} by i

∴  \sqrt{-2}=\sqrt{2}*i

∴  \sqrt{-2}=\sqrt{2}i

∴ The roots of the equation are \sqrt{2}i and  -\sqrt{2}i

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Rewriting the whole as an Equivalent Fraction :

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Rewrite the whole as a fraction using  a  as the denominator :

         20     20 • a

   20 =  ——  =  ——————

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Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

(3x-4a) - (20 • a)     3x - 24a

——————————————————  =  ————————

        a                 a    

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Pulling out like terms :

4.1     Pull out like factors :

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Step  5  :

When a fraction equals zero :

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Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

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Graph of a Straight Line :

 

 

Calculate the Y-Intercept :

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   Slope     =  0.250/2.000 =  0.125  

Geometric figure: Straight Line

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Step-by-step explanation:

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