how can i solve the nature of the roots of this quadratic??

Question

how can i tell which one is which???

5x2 + 10x = -5

one real double root
two real distinct roots/solutions
no real roots

Answer 1

5x^2+10x+5=0
Delta=100-4(5)(5)=100-100=0
So you have one real double root
[-10+(-)0]/10=-1

Answer 2

Put it into a form so that it's equal to zero
5x^2 + 10x + 5 = 0

then use the quadratic formula:
roots = (-b +/- sqrt(b^2 - 4*a*c)) / (2*a)

where a is the coefficient for the x^2 term, b is the coefficient for the x term, and c is the third term.
a = 5
b = 10
c = 5

Plugging these values into the quadratic formula, we get:
roots = (-10 +/- sqrt(10^2 - 4*5*5)) / (2*5)
roots = (-10 +/- sqrt(100 - 100)) / (10)
roots = (-10 +/- sqrt(0)) / (10)
roots = (-10 +/- 0) / (10)
roots = -10/10
roots = -1

Since the term inside the square root is zero, we have plus-or-minus zero, meaning there is one real root, and it's a double root.

Answer 3

Simplify by dividing by 5:

x2 + 2x = -1

now move everything over:

x2 + 2x + 1 = 0

This is factorable into:

(x + 1)^2 = 0

or (x+1)(x+1) = 0

so -1 is a solution twice, hence it is a double root.

Two distinct roots would be factored into something like:
(x-1)(x+2) = 0
which has 1 and -2 as roots.

No real roots would be something that isn't factorable.

Answer 4

If you move everything to the left side and divide by 5, you get x^2+2x+1, which looks alot like (x+1)^2 factored. So you have a real double root.

Answer 5

5x² + 10x = -5

add 5 to both sides

5x² + 10x + 5 = 0

divide thru by 5

x² + 2x + 1 = 0

(x + 1)² = 0

(x + 1)(x + 1) = 0

one real double root

x = -1
.

Answer 6

add 5 for both sides to set the equation equal to 0
5x^2 + 10x + 5 = 0

use discriminant, b^2 - 4ac, to determine how many solutions a quadratic has

if b^2 - 4ac > 0 , there are 2 solutions
if b^2 - 4ac = 0, there is 1 solution
if b^2 - 4ac < 0, there is no solution

standard form:
ax^2 + bx + c = 0

a = 5
b = 10
c = 5

10^2 - 4(5)(5)
10^2 - 100
100 - 100
0

there is 1 solution

Answer 7

5x^2 + 10x + 5 = 0
try to factor, but doesn't work. So, the possible factors might be 5/5 or 5, but those don't work and so they must not be real.

Answer 8

use b^2 - 4ac

positive value figure means 2 distinct roots

zero value means one real double root

and value negative means no real roots