What is the discriminant of quadratic equation x^2+11x+121=x+96?
We have to find the discriminant of x^2+11x+121=x+96.
Now discriminant of ax^2 + bx + c = 0 is given by b^2 - 4ac.
=> x^2 + 11x - x + 121 -96 = 0
=> x^2 + 10 x - 25
so a = 1 , b = 10 and c = 25
The discriminant is 10^2 - 4*1*25
= 100 - 100 = 0
Therefore the discriminant is 0.
First of all, you need to set up the problem into the `ax^2 + bx + c`
`x^2 + 11 x + 121 = x + 96`
`x^2 + 11x + 35 = x` Subtract 96 from both sides
`x^2 + 10x + 35 = 0` Subtracting x to both sides to make it in the proper form.
Now we must distinguish which is a, b, and c
`a = 1`
`b = 10`
`c = 35` The discriminant formula is `b^2 - 4ac`
`(10)^2 - 4(1)(35)`
`100 - 140`
After plugging it into the equation, our discriminant is -140. When graphing, this means there are no real roots.
The given equation is x^2+11x+121=x+96.
Before finding the discriminant of the equation, we write the equation in the standard form ax^2+bx+c= o whose discriminant D is given by: D = (b^2-4ac).
x^2+11x+121=x+96 is rearranged as: x^2+11x+121-x-96.
=> x^2 +10x +25, which is like ax^2+bx+c.
=> a=1, b= 10 and c= 25.
So D = b^2-4ac = (10^2-4*1*25) = 0.
So the discriminant of the given equation is 0.
Before determining the discriminant, we'll move all terms to the left side:
x^2+11x+121-x-96 = 0
We'll combine like terms:
x^2 + 10x + 25 = 0
We'll write the formula of discriminant:
delta = b^2 - 4ac
We'll identify the coefficients a,b,c:
a = 1, b = 10 , c = 25
delta = 100 - 4*25
delta = 100 - 100
delta = 0
The discriminant of quadratic equation is delta = 0.