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patriot [66]
2 years ago
15

Select the two values of x that are roots of this equation x^2-5x+2=0

Mathematics
1 answer:
Nataly [62]2 years ago
3 0

The roots of the equation is x = 4.56 OR x = 0.44

<h3>Quadratic equation</h3>

From the question, we are to determine the roots of the given equation

The given equation is

x² -5x +2 = 0

Using the formula method,

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

In the given equation,

a = 1, b = -5, c = 2

Putting the values into the formula,

x =\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(2) } }{2(1)}

x =\frac{5 \pm \sqrt{25-8} }{2}

x =\frac{5 \pm \sqrt{17} }{2}

x =\frac{5 + \sqrt{17} }{2} OR x =\frac{5 - \sqrt{17} }{2}

x =\frac{5 + 4.12}{2} OR x =\frac{5 - 4.12}{2}

x =\frac{9.12}{2} OR x =\frac{0.88}{2}

x = 4.56 OR x = 0.44

Hence, the roots of the equation is x = 4.56 OR x = 0.44

Learn more on Quadratic equation here: brainly.com/question/8649555

#SPJ1

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Find equation of set of points pieces that its distance from the point 3, 4, -5 and -2, 1, 4 are equal.
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Answer:

Step-by-step explanation:

Suppose we a point P(x,y,z) such that its distance from either the point A(3,4,-5) or B(-2,1,4) is the same.

Using this information we can formula:

distance AP = distance BP

first, let's find the distance from AP, using the distance formula.

r = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2}

AP = \sqrt{(3 - x_2)^2 + (4 - y_2)^2 + (-5 - z_2)^2}

similarly, we can find the distance BP

BP = \sqrt{(-2 - x_2)^2 + (1 - y_2)^2 + (4 - z_2)^2}

since both distances are exactly the same we can equate them

AP = BP

\sqrt{(3 - x_2)^2 + (4 - y_2)^2 + (-5 - z_2)^2} = \sqrt{(-2 - x_2)^2 + (1 - y_2)^2 + (4 - z_2)^2}

we can simplify it a bit squaring both sides, and getting rid of the subscripts.

(3 - x)^2 + (4 - y)^2 + (-5 - z)^2 = (-2 - x)^2 + (1 - y)^2 + (4 - z)^2

what we have done here is formulated an equation which consists of any point P that will have the same distance from (3,4,-5) and (-2,1,4).

To put it more concretely,

This is the equation of the the plane from that consists of all points (P) from which the distance from both (3,4,-5) and (-2,1,4) are equal.

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3 years ago
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