Im doing a quadratics project, and keep getting a zero within my "b squared-4ac"now what?

Question

a=1 b=6 c=9, my rgade is riding on this project, and i cant figure out what to do!

Answer 1

it is quite possible to get zero with the discriminant(b^2-4ac).just recall that the square root of 0 is 0.this simply means that the quadratic equation that you have has equal roots(in the case a=1,b=6 and c=9 the root is -3 and -3).the quadratic expression that you have then is a "perfect square trinomial".

Answer 2

Hence the eqn is ax^2 + bx +c i.e x^2+6x+9
This eqn does not require the quadratic eqn to be solved divide 6x as 3x+3x
we get
x^2 + 3x + 3x +9
=>x(x+3) + 3(x+3)
=> (x+3)^2=0
Hence x=-3
this is a trivial solution and b squared -4ac coming zero implies that the roots of the eqn are real and not imaginary that's all.

Answer 3

Not sure exactly what your project is, but sometimes you will get a zero as the discriminant (b^2-4ac). When you use the quadratic equation to solve a polynomial and you get zero as the discriminant, you will get two answers as you always do, but they will be the same. In the case of your example, you should get solutions of -3 and -3.

Answer 4

I'm not sure what you question is, but all that b squared-4ac=0 means is that the solution to the quadratic equation only has one solution. Another way of saying that is that the graph of the function only touches the x-axis at one point.

Answer 5

First, recognize that b^4 - 81 is not a perfect square. It's a difference of two squares [(b²)², and 81 = 9²]. Therefore (b^4 - 81) factors out to (b² + 9)(b² - 9). However b² - 9 is itself a difference of squares. So the complete factorization of this expression is (b^4 - 9) = (b² + 9)(b + 3)(b - 3)

Answer 6

you have an equation of the form:
x^2 + 6x + 9 = 0

when your (b^2 - 4ac) term equals 0, that means you can factor the polynomial:

(x + 3)(x + 3) = x^2 + 6x +9 -----> x = -3 (it's a double root)

Answer 7

you can have zero as an answer because the square root of 0 is 0 then just plug 0 into the rest of the quad equation

Answer 8

use the non zero terms
x = -b / 2a
which gives you -6/2 = -3
answer ..x1 = -3, x2 = -3
or the equation is
(x+3)^2 which turns ot to be x^2 + 6x + 9...same coefficients as you defined in the question

Answer 9

just keep going. the square root of zero is simply zero.

Answer 10

It means there's only one root of the polynomial. If you graph the corresponding parabola its vertex will be on the x-axis.