what is the discriminant in the quadratic equation x^2+11x+121=x+96?

Answer 1

First, change it to a normal quadratic equation.

x^2 + 10x + 25 = 0

Now, you should know the quadratic formula...
x = ( -b ±√(b^2 - 4ac)) / 2a

The discriminant is everything under the radical, which is...

b^2 - 4ac

When you have a quadratic equation, you can see it in all variables, like this:
ax^2 + bx + c = 0

Now, plug in the numbers from your quadratic into your discriminant formula.

x^2 + 10x + 25 = 0

10^2 - 4(1)(25)
100 - 100 = 0

The discriminant for your equation is zero.

Answer 2

First rewrite this into standard form

Ax^2 + Bx + C = 0

x^2 + 11x + 121 = x + 96 => x^2 +10x + 25 = 0

For a quadratic in standard form the discriminant is

B^2 - 4AC

In our case A = 1, B = 10, C = 25

So

Discriminant = 10^2 - 4 * 1 * 25 = 0

This means that we have exactly one root.

You will notice the polynomial factors as

x^2 + 10x + 25 = (x+5)^2

which means x = -5 is a double root

Answer 3

Rewriting the equation in the standard quadratic form x^2+10x+25=0
D= b^2-4ac=10^2-(4)(1)(25)=100-100=0

Answer 4

x^2 + 11x + 121 = x + 96
x^2 + 10x + 25 = 0

d = b^2 - 4ac

d = 10^2 - 4(1)(25)
d = 100 - 100
d = 0

Answer 5

x^2 + 10x + 25 = 0

D = 10^2 - 4*1*25

D = 100 - 100

D = 0

Answer 6

reduce it to x^2 + 10x + 25 = 0

Now you have a normalized equation.

Answer 7

to find a discriminatn, you just need the formulae:
D = b^2 - 4ac

Answer 8

zero