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3 years ago

6

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

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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A piece of cardboard has the dimensions (x + 15) inches by (x) inches with the area of 60 in 2 . Write the quadratic equation th

pochemuha

Answer:

$x^2 + 15x - 60 = 0$

The actual dimension is 18.28 by 3.28

Step-by-step explanation:

Given

Dimension:

$(x + 15)\ by\ x$

$Area = 60in^2$

Required

Determine the quadratic equation and get the possible values of x

Solving (a): Quadratic Equation.

The cardboard is rectangular in shape.

Hence, Area is calculated as thus:

$Area = Length * Width$

$60= (x + 15) * x$

Open Bracket

$60= x^2 + 15x$

Subtract 60 from both sides

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<em>Hence, the above represents the quadratic equation</em>

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First, we need to solve for x

This can be solved using quadratic formula:

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$c = -60$

So:

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-15 \± \sqrt{15^2 - 4*1*-60}}{2*1}$

$x = \frac{-15 \± \sqrt{225 + 240}}{2}$

$x = \frac{-15 \± \sqrt{465}}{2}$

$x = \frac{-15 \± \21.56}{2}$

Split:

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