Understanding Quadratic Equations - Math

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Question

Given $2x^{2}+3x-5=0$ , what is the value of the discriminant?

Answer

In general, the discriminant is $b^{2}-4ac$ .

In this particual case .

Plug in these three values and simplify: $(3)^{2}-4(2)(-5)= 49$

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Question

Use the discriminant to determine the nature of the roots:

Answer

The formula for the discriminant is:

Since the discriminant is negative, there are imaginary roots.

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Question

Use the discriminant to determine the nature of the roots:

Answer

The formula for the discriminant is:

$=1200^{}$

Since the discriminant is positive and not a perfect square, there are irrational roots.

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Question

Use the discriminant to determine the nature of the roots:

Answer

The formula for the discriminant is:

Since the discriminant is negative, there are imaginary roots.

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Question

Given $2x^{2}+3x-5=0$ , what is the value of the discriminant?

Answer

In general, the discriminant is $b^{2}-4ac$ .

In this particual case .

Plug in these three values and simplify: $(3)^{2}-4(2)(-5)= 49$

Compare your answer with the correct one above

Question

Use the discriminant to determine the nature of the roots:

Answer

The formula for the discriminant is:

Since the discriminant is negative, there are imaginary roots.

Compare your answer with the correct one above

Question

Use the discriminant to determine the nature of the roots:

Answer

The formula for the discriminant is:

$=1200^{}$

Since the discriminant is positive and not a perfect square, there are irrational roots.

Compare your answer with the correct one above

Question

Use the discriminant to determine the nature of the roots:

Answer

The formula for the discriminant is:

Since the discriminant is negative, there are imaginary roots.

Compare your answer with the correct one above

Question

Given $2x^{2}+3x-5=0$ , what is the value of the discriminant?

Answer

In general, the discriminant is $b^{2}-4ac$ .

In this particual case .

Plug in these three values and simplify: $(3)^{2}-4(2)(-5)= 49$

Compare your answer with the correct one above

Question

Use the discriminant to determine the nature of the roots:

Answer

The formula for the discriminant is:

Since the discriminant is negative, there are imaginary roots.

Compare your answer with the correct one above

Question

Use the discriminant to determine the nature of the roots:

Answer

The formula for the discriminant is:

$=1200^{}$

Since the discriminant is positive and not a perfect square, there are irrational roots.

Compare your answer with the correct one above

Question

Use the discriminant to determine the nature of the roots:

Answer

The formula for the discriminant is:

Since the discriminant is negative, there are imaginary roots.

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Question

Solve the following equation using the quadratic form:

Answer

Factor the equation and solve:

$x = \pm \sqrt{3}$

or

$x = \pm i\sqrt{3}$

Therefore there are four answers:

$x=\pm\sqrt{3}, \pm i\sqrt{3}$

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Question

Solve the following equation using the quadratic form:

$x-4\sqrt{x}-45=0$

Answer

Factor the equation and solve:

$x-4\sqrt{x}-45=0$

$(\sqrt{x}-9)(\sqrt{x}+5)=0$

$\sqrt{x}=9$

or

$\sqrt{x}=-5$

This has no solutions.

Therefore there is only one answer:

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Question

Given $2x^{2}+3x-5=0$ , what is the value of the discriminant?

Answer

In general, the discriminant is $b^{2}-4ac$ .

In this particual case .

Plug in these three values and simplify: $(3)^{2}-4(2)(-5)= 49$

Compare your answer with the correct one above

Question

Use the discriminant to determine the nature of the roots:

Answer

The formula for the discriminant is:

Since the discriminant is negative, there are imaginary roots.

Compare your answer with the correct one above

Question

Use the discriminant to determine the nature of the roots:

Answer

The formula for the discriminant is:

$=1200^{}$

Since the discriminant is positive and not a perfect square, there are irrational roots.

Compare your answer with the correct one above

Question

Use the discriminant to determine the nature of the roots:

Answer

The formula for the discriminant is:

Since the discriminant is negative, there are imaginary roots.

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Question

Solve the equation for .

$\small \frac{1}{x}=\frac{x+1}{6}$

Answer

$\small \small \frac{1}{x}=\frac{x+1}{6}$

Cross multiply.

$\small 6=x(x+1)$

$\small 6=x^2+x$

Set the equation equal to zero.

$\small 0=x^2+x-6$

Factor to find the roots of the polynomial.

and

$\small 0=(x+3)(x-2)$

$\small 0=x+3; x=-3$

$\small 0=x-2; x=2$

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Question

Evaluate $(2x+3)^{2}$

Answer

In order to evaluate $(2x+3)^{2}$ one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms.

$\dpi{100} (2x+3)^{2}=(2x+3)(2x+3)$

Multiply terms by way of FOIL method.

Now multiply and simplify.

$=4x^{2}+6x+6x+9$

$\rightarrow 4x^{2}+12x+9$

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