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Quadratic Equations

Identify whic...

Question

Identify which of the following is/are a quadratic polynomial function:

f (x) = (x + 1)^{3} - (x + 2)^{3}

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g (x) = \frac{x^{4}}{x^{2}}

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h (x) = (x + 1)^{2} - (x + 2)^{2}

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All of these

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Solution

The correct options are
A $f (x) = (x + 1)^{3} - (x + 2)^{3}$
B
$g (x) = \frac{x^{4}}{x^{2}}$

Option 1) $f (x) = (x + 1)^{3} - (x + 2)^{3}$
$= x^{3} + 1 + 3 x (x + 1) - x^{3} + 8 + 6 x (x + 2)$
$= x^{3} + 1 + 3 x^{2} + 3 x - x^{3} - 8 - 6 x^{2} - 12 x$
The power of $x^{3}$ cancels out and results in to quadratic equation.
Option 2) g(x) = $x^{2}$
Option 3) $x^{2} + 1 + 2 x - x^{2} - 4 - 8 x$
The power of $x^{2}$ cancels out which doesn't result in to quadratic equation.

Suggest Corrections

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f (x)

g (x)

h (x)

h (x) = f (x) - g (x) \forall x \in R .

h (x) = 0

x = - 3

h (- 1) = 6,

h (5)

(\sqrt{x})^{2}

= \frac{x^{2}}{x}

A = \{x : - 1 \leq x \leq 1\}

f (x) = \frac{x}{2}

g (x) = \sin (\frac{π x}{2})

h (x) = | x |

k (x) = x^{2}

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