The table below shows the amount paid for different numbers of items.

Find the value of p if the following pair of equation may have one root common:

Diano4ka-milaya [45]

The value of p if the pair of equations may have one root common is 1.

<h3>What are the roots of the equation?</h3>

Let the equation be ax² + bx + c = 0.

Then the roots of the equation will be

$\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}$

The equations are given below.

2x² + px - 1 = 0 and 3x² - 2x - 5 = 0

The roots of the equation 3x² - 2x - 5 = 0 will be

3x² - 5x + 3x - 5 = 0

(3x - 5)(x + 1) = 0

x = -1, 5/3

At x = -1, the value of p will be

2(-1)² + p(-1) - 1 = 0

2 - p - 1 = 0

p = 1

The value of p if the pair of equations may have one root common is 1.

More about the roots of the equation link is given below.

brainly.com/question/12029673

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7 0

2 years ago

Please help me I will give you the brain thing and extra points (image below) 4/5

bekas [8.4K]

A. 1 mile per minute

7 0

3 years ago

Read 2 more answers

The dimensions of a rectangular garden were 4m by 5m. Each dimension was increased by the same amount the garden then had an are

pogonyaev

The dimension of new garden is 7 meter by 8 meter

Solution:

The dimensions of a rectangular garden were 4m by 5m

Length = 4 m

Width = 5 m

Each dimension was increased by the same amount the garden then had an area of 56 square meter

Let "x" be the amount of increase

Then,

Length = 4 + x

Width = 5 + x

Also, given that,

New area = 56 square meter

The area of rectangle is given as:

$Area = length \times width$

Substituting the values we get,

$56 = (4+x)(5+x)\\\\56 = 20 + 4x + 5x + x^2\\\\x^2 + 9x + 20 - 56 = 0\\\\x^2 + 9x -36=0$

Let us solve the above equation by quadratic formula

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Using the above formula,

$\text{For } x^2+9x-36 \text{ we get , }$

a = 1 and b = 9 and c = -36

Substituting the values of a = 1 ; b = 9 ; c = -36 in above quadratic formula we get,

$x = \frac{-9\pm \sqrt{9^2-4\cdot \:1\left(-36\right)}}{2\cdot \:1}\\\\x = \frac{-9\pm \sqrt{81+144}}{2}\\\\x = \frac{-9 \pm 15}{2}$

We get two solutions,

$x = \frac{-9+15}{2} \text{ or } x = \frac{-9-15}{2}\\\\x = 3 \text{ or } x = -12$

Since dimension cannot be negative, ignore x = -12

Thus solution is x = 3

Length = 4 + x = 4 + 3 = 7

Width = 5 + x = 5 + 3 = 8

Thus dimension of new garden is 7 meter by 8 meter

5 0

3 years ago

3. A rock is thrown from the top of a tall building. The distance, in feet, between

lakkis [162]

Answer:

124

Step-by-step explanation:

4 0

4 years ago

What is the answer when you round 522 254 to the nearest 10

DiKsa [7]

Answer:

522250

How to round to the nearest tenth:

Whenever you want to round a number to a particular digit, look only at the digit immediately to its right. For example, if you want to round to the nearest tenth, look to the right of the tenths place: This would be the hundredths place digit. Then, if it is 5 or higher, you get to add one to the tenths digit. If it is 4 or lower, the tenths digit remains the same.

For example, 3.58 can be rounded to 3.6 because the hundredths place digit, 8 is greater than or equal to 5.

3.32 would be rounded to 3.3, because the hundredths place digit, 2, is less than 5.

6 0

3 years ago