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Allisa [31]
3 years ago
5

Solve the polynomial inequality x^2-3x-10>0

Mathematics
1 answer:
djverab [1.8K]3 years ago
7 0

As x² - 3x - 10 factors, we can use the zero product property and pull it apart into factors. It factors because 2 and 5 have a difference of 3 and product of 10

x² - 3x - 10 > 0

(x - 5)(x + 2) > 0

To find where the inequality is true, we use a sign test. When x-5 > 0, it means x >5, and 5 is one of our sign test values. Similarly, -2 is the other. We can then make three intervals - A (less than -2), B (between -2 and 5), and C (more than 5).

<--------------- -2 ------------------ 5 -------------------------->

A B C

To do a sign test, we choose values to see what happens. First, test x = -5.

(-5 - 5)(-5 + 2) = (-10)(-3) = 30. Because 30 > 0, the inequality is true for x < -2. So interval A is true.

Next, test x = 0.

(0 - 5) (0 + 2) = (-5)(2) = -10. Because -10 < 0 is false, the inequality is false for x > -2 and x < 5. So interval B is false.

Last, test x = 10

(10 - 5) (10 + 2) = (5) (8) = 40. Because 40 > 0 is true, the inequality is true for x > 5. So interval C is true.

We put the true intervals together.

(-∞, -2) ∪ (5, ∞) is where this inequality is true,

{x : x < -2 or x > 5} is also how it's said in set notation.

You might be interested in
The vertices of a triangle are A(1, –9), B(0, –3), C(–4, –5). Fine the length of each side. What type of triangle is triangle AB
Alenkinab [10]

Answer:

AB = √37

BC = 2√5

AC = √41

Type: SCALENE TRIANGLE

Step-by-step explanation:

Given the coordinates

A(1, –9), B(0, –3), C(–4, –5)

We are to find the length of each sides first. Using the formula for calculating the distance between two points, we will have;

For A(1, –9) and B(0, –3)

AB = √(-3+9)²+(0-1)²

AB = √6²+(-1)²

AB = √36+1

AB = √37

For coordinates B(0, –3) and C(–4, –5)

BC = √(-5+3)²+(-4-0)²

BC= √(-2)²+(-4)²

BC = √4+16

BC = √20

BC = 2√5

For coordinates  A(1, –9), C(–4, –5)

AC = √(-5+9)²+(-4-1)²

AC= √(4)²+(-5)²

AC = √16+25

AC = √41

<em>Since the sides of the triangles are all different, hence the triangle is a SCALENE triangle</em>

8 0
3 years ago
Question 3 (1 point)
den301095 [7]

Answer: Pay 250 per month until it’s paid off

4 0
3 years ago
Someone please help me
allsm [11]

Answer:

Solutions: x = \frac{-3}{ 4} + i \sqrt{39},  x = \frac{-3}{4} - i \sqrt{39}

Step-by-step explanation:

Given the quadratic equation, 2x² + 3x + 6 = 0, where a =2, b = 3, and c = 6:

Use the <u>quadratic equation</u> and substitute the values for a, b, and c to solve for the solutions:

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

x = \frac{-3 +/- \sqrt{3^{2} - 4(2)(6)} }{2(2)}

x = \frac{-3 +/- \sqrt{9- 48} }{4}

x = \frac{-3 +/- \sqrt{-39} }{4}

x = \frac{-3 + i \sqrt{39} }{4}, x = \frac{-3 - i \sqrt{39} }{4}

Therefore, the solutions to the given quadratic equation are:

x = -\frac{3}{ 4} + i \sqrt{39} ,   x = -\frac{3}{4} - i \sqrt{39}

4 0
2 years ago
action bar. John has $132.55 in his bank account. He wants to join a guitar class that charges a $15 fee every week. John plans
Artemon [7]
$132.55-($15*12)=$132.55-$180=$-47.45
So then he would have owed 47.45 dollars!
5 0
3 years ago
Read 2 more answers
if the hypotenuse of a special triangle of 45 45 90 was 10 radical 6 how would u solve for the hypotenuse
Vinvika [58]
Just do it it’s quite easy
3 0
3 years ago
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