can i get help with this please what does it mean type of root

Determine the number and type of roots

2X(X+2) =-2

roots are also knows as zeros or x-intercepts ,so solve for x

to examine the type of roots and find the number of roots be look at the determinant b^2 - 4ac

2x^2 + 4x + 2 = 0
or
x^2 + 2x + 1 = 0

the solution is so blatantly obvious,
(x+1)^2=0
x+1=0
x = -1

it was simpler to actually find the root

anyway .....
b^2 - 4ac = 4 -4(1)(1) = 0
so one real root, which we found

Of course, I can help you with that.

To determine the number and type of roots of the equation 2X(X+2) = -2, we first need to simplify the equation.

1. Start by expanding the expression on the left side of the equation using the distributive property.

2X(X + 2) = -2
2X^2 + 4X = -2

2. Now, bring all the terms to one side of the equation to form a quadratic equation in standard form (ax^2 + bx + c = 0).

2X^2 + 4X + 2 = 0

Now, we can determine the number and type of roots by examining the discriminant (b^2 - 4ac) of this quadratic equation.

In this case, a = 2, b = 4, and c = 2.

3. Calculate the discriminant (D) using the formula D = b^2 - 4ac.

D = (4)^2 - 4(2)(2)
= 16 - 16
= 0

Since the discriminant is equal to 0, the equation has exactly one root.

4. Now, let's determine the type of root. Different values of the discriminant represent different types of roots:

i. If D > 0, the equation has two distinct real roots.
ii. If D = 0, the equation has one real root (also known as a double root).
iii. If D < 0, the equation has two complex roots.

In this case, since D = 0, the equation has one real root (a double root).

Therefore, the number of roots is one, and the type of root is a double root.

I hope this helps you understand how to determine the number and type of roots for a quadratic equation. Let me know if you have any other questions!