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3 years ago

Consider the quadratic equation x squared = 4x - 5. how many solutions does the equation have?

Mathematics

1 answer:

snow_lady [41]3 years ago

5 0

Answer:

The quadratic equation has two complex solutions

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2}=4x-5$

Equate to cero

$x^{2}-4x+5=0$

$a=1\\b=-4\\c=5$

substitute in the formula

$x=\frac{4(+/-)\sqrt{-4^{2}-4(1)(5)}} {2(1)}$

$x=\frac{4(+/-)\sqrt{16-20}} {2}$

$x=\frac{4(+/-)\sqrt{-4}} {2}$

Remember that

$i^{2}=-1$

$x=\frac{4(+/-)2i} {2}$

$x=2(+/-)i$

therefore

The quadratic equation has two complex solutions

You might be interested in

-3/5x - 7/20x + 1/4x= -56

romanna [79]

Answer:

x = 80

Step-by-step explanation:

Combine − 3/5x and 7/20x to get -19/20x.

Then combine -19/20x and 1/4x and you get -7/10x.

Then you multiply both sides by -10/7 which is the reciprocal of -7/10.

Make -56(-10) one fraction.

Multiply -56 and -10 and you get 560.

Then divide 560 by 7 to get 80.

8 0

3 years ago

Read 2 more answers

What is the decimal that is equivalent to the expression 3 * 100 + 7 * 10 + 4 * 1 + 6 * 0.01 + 1 * 0.001

barxatty [35]

I believe it is 0.0318

5 0

3 years ago

PLEASE HELP 100 POINTS!!!!!!

horrorfan [7]

Answer:

A) See attached for graph.

B) (-3, 0) (0, 0) (18, 0)

C) (-3, 0) ∪ [3, 18)

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

$g(x)=\begin{cases}x^3-9x \quad \quad \quad \quad \quad \textsf{if }x < 3\\-\log_4(x-2)+2 \quad \textsf{if }x\geq 3\end{cases}$

Therefore, the function has two definitions:

$g(x)=x^3-9x \quad \textsf{when x is less than 3}$

$g(x)=-\log_4(x-2)+2 \quad \textsf{when x is more than or equal to 3}$

When graphing piecewise functions:

Use an open circle where the value of x is not included in the interval.
Use a closed circle where the value of x is included in the interval.
Use an arrow to show that the function continues indefinitely.

First piece of function

Substitute the endpoint of the interval into the corresponding function:

$\implies g(3)=(3)^3-9(3)=0 \implies (3,0)$

Place an open circle at point (3, 0).

Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.

Second piece of function

Substitute the endpoint of the interval into the corresponding function:

$\implies g(3)=-\log_4(3-2)+2=2 \implies (3,2)$

Place an closed circle at point (3, 2).

Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attached for graph.

The x-intercepts are where the curve crosses the x-axis, so when y = 0.

Set the first piece of the function to zero and solve for x:

$\begin{aligned}g(x) & = 0\\\implies x^3-9x & = 0\\x(x^2-9) & = 0\\\\\implies x^2-9 & = 0 \quad \quad \quad \implies x=0\\x^2 & = 9\\\ x & = \pm 3\end{aligned}$

Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.

Set the second piece to zero and solve for x:

$\begin{aligned}\implies g(x) & =0\\-\log_4(x-2)+2 & =0\\\log_4(x-2) & =2\end{aligned}$

$\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b$

$\begin{aligned}\implies 4^2&=x-2\\x & = 16+2\\x & = 18 \end{aligned}$

Therefore, the x-intercept for the second piece is (18, 0).

So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).

From the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.

Interval notation: (-3, 0) ∪ [3, 18)

Learn more about piecewise functions here:

brainly.com/question/11562909