Question

© Divide which of the following are quadratic equations:
x²+5x-2=0​

Answer 1

Step-by-step explanation:

ya Allah help us to the sum of money and I will

Answer 2

Step-by-step explanation:

1.1 Factoring x2-5x-2

The first term is, x2 its coefficient is 1 .

The middle term is, -5x its coefficient is -5 .

The last term, "the constant", is -2

Step-1 : Multiply the coefficient of the first term by the constant 1 • -2 = -2

Step-2 : Find two factors of -2 whose sum equals the coefficient of the middle term, which is -5 .

-2 + 1 = -1

-1 + 2 = 1

Equation at the end of step

1

:

x2 - 5x - 2 = 0

STEP

2

:

Parabola, Finding the Vertex:

2.1 Find the Vertex of y = x2-5x-2

.

Note that the square root of

(x-(5/2))2 is

(x-(5/2))2/2 =

(x-(5/2))1 =

x-(5/2)

Now, applying the Square Root Principle to Eq. #2.2.1 we get:

x-(5/2) = √ 33/4

Add 5/2 to both sides to obtain:

x = 5/2 + √ 33/4

Since a square root has two values, one positive and the other negative

x2 - 5x - 2 = 0

has two solutions:

x = 5/2 + √ 33/4

or

x = 5/2 - √ 33/4

Note that √ 33/4 can be written as

√ 33 / √ 4 which is √ 33 / 2

Solve Quadratic Equation using the Quadratic Formula

2.3 Solving x2-5x-2 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 1

B = -5

C = -2

Accordingly, B2 - 4AC =

25 - (-8) =

33