Given:
The equation is

To find:
The number of roots and discriminant of the given equation.
Solution:
We have,

The highest degree of given equation is 2. So, the number of roots is also 2.
It can be written as

Here,
.
Discriminant of the given equation is





Since discriminant is
, which is greater than 0, therefore, the given equation has two distinct real roots.
Answer:
x = -5, 5
Step-by-step explanation:
-x^2-8=-33
Add 8 to each side
-x^2-8+8=-33+8
-x^2 = -25
Divide each side by -1
x^2 = 25
Take the square root of each side
sqrt(x^2) = ±sqrt(25)
x = ±5
Answer by answer key by key question equals equation
Answer:
4 cm and 7 cm
Step-by-step explanation:
Given that Juanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm.
We know that opposite sides are equal in a parallelogram.
Hence we have

Hence the side length = 
The adjacent side = 
Thus answer is 4 cm and 7 cm
Answer:
x = 2√2
y = 2√6
Step-by-step explanation:
Consider the ratio of the two legs of the two smaller interior right triangles. (refer to attached diagrams for the triangles - I have outlined one in blue and the other in red)
These will be equal since the triangles are similar
shorter leg : longer leg
(blue triangle = red triangle)
⇒ x : 4 = 2 : x
⇒ x/4 = 2/x
⇒ x² = 8
⇒ x = √8
⇒ x = 2√2
Now we have x, we have the two legs of the right triangle with hypotenuse labelled y.
Using Pythagoras' Theorem a² + b² = c² (where a and b are the legs and c is the hypotenuse)
⇒ 4² + (2√2)² = y²
⇒ y² = 24
⇒ y = √24
⇒ y = 2√6