Hi can someone please answer my question please don't put random letters. thank you ❤️

One of the roots of the quadratic equation dx^2+cx+p=0 is twice the other, find the relationship between d, c and p

scZoUnD [109]

Answer:

$c^2 = 9dp$

Step-by-step explanation:

Given

$dx^2 + cx + p = 0$

Let the roots be $\alpha$ and $\beta$

So:

$\alpha = 2\beta$

Required

Determine the relationship between d, c and p

$dx^2 + cx + p = 0$

Divide through by d

$\frac{dx^2}{d} + \frac{cx}{d} + \frac{p}{d} = 0$

$x^2 + \frac{c}{d}x + \frac{p}{d} = 0$

A quadratic equation has the form:

$x^2 - (\alpha + \beta)x + \alpha \beta = 0$

So:

$x^2 - (2\beta+ \beta)x + \beta*\beta = 0$

$x^2 - (3\beta)x + \beta^2 = 0$

So, we have:

$\frac{c}{d} = -3\beta$ -- (1)

and

$\frac{p}{d} = \beta^2$ -- (2)

Make $\beta$ the subject in (1)

$\frac{c}{d} = -3\beta$

$\beta = -\frac{c}{3d}$

Substitute $\beta = -\frac{c}{3d}$ in (2)

$\frac{p}{d} = (-\frac{c}{3d})^2$

$\frac{p}{d} = \frac{c^2}{9d^2}$

Multiply both sides by d

$d * \frac{p}{d} = \frac{c^2}{9d^2}*d$

$p = \frac{c^2}{9d}$

Cross Multiply

$9dp = c^2$

or

$c^2 = 9dp$

Hence, the relationship between d, c and p is: $c^2 = 9dp$

8 0

3 years ago

1. (x + 2) < −3(x + 4) 2. −3x + 3 < 6

Leno4ka [110]

number 1:

$x>\frac{-7}{2}$

number 2:

$x>-1$

7 0

3 years ago

A cube has a side length of x feet. Which expression represents the surface area of the cube?

alexdok [17]

The answer is D)6x2 square units.

A surface area of a cube is a sum of its sides' areas. A side of the cube is a square, and there are total 6 sides of the cube. Also, an area of the side of the cube is the area of the square, which can be expressed as a², where a is the length of the side. Therefore, the surface area (SA) of the cube is:
SA = 6*a² = 6a²

If side length is x, that means that a = x units.
After replacing it in the formula, you will have:
SA = 6a² = 6x² square units

8 0

4 years ago

Read 2 more answers

Four friends split equally a lunch bill of 36.96 plus 20% tip. How much did each person pay

castortr0y [4]

Let P = how much each person paid.

P = [(36.96)(0.20) + 36.96]/4

Solve for P to find your answer.

8 0

3 years ago

What is the first step in solving the equation x2 – 16/25 = 0?

Keith_Richards [23]

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x^2-(16/25)=0

Step by step solution :Step 1 : 16 Simplify —— 25 Equation at the end of step 1 : 16 (x2) - —— = 0 25 Step 2 :Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 25 as the denominator :

x2 x2 • 25 x2 = —— = ——————— 1 25

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x2 • 25 - (16) 25x2 - 16 —————————————— = ————————— 25 25 Trying to factor as a Difference of Squares :

2.3 Factoring: 25x2 - 16

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =
 A2 - AB + BA - B2 =
 A2 - AB + AB - B2 =
 A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 25 is the square of 5
Check : 16 is the square of 4
Check : x2 is the square of x1 

Factorization is : (5x + 4) • (5x - 4)

Equation at the end of step 2 : (5x + 4) • (5x - 4) ——————————————————— = 0 25 Step 3 :When a fraction equals zero : 3.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

(5x+4)•(5x-4) ————————————— • 25 = 0 • 25 25

Now, on the left hand side, the 25 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
(5x+4) • (5x-4) = 0

Theory - Roots of a product :

3.2 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

3.3 Solve : 5x+4 = 0

Subtract 4 from both sides of the equation :
 5x = -4
Divide both sides of the equation by 5:
 x = -4/5 = -0.800

Solving a Single Variable Equation :

3.4 Solve : 5x-4 = 0

Add 4 to both sides of the equation :
 5x = 4
Divide both sides of the equation by 5:
 x = 4/5 = 0.800

x = 4/5 = 0.800
 x = -4/5 = -0.800

3 0

3 years ago

Read 2 more answers

Hi can someone please answer my question please don't put random letters. thank you ❤️​

Hi can someone please answer my question please don't put random letters. thank you ❤️