Question

Help with the discriminant formula?

Answer 1

ill see what i can do

Answer 2

I have to find the value of the discriminant using the discriminant formula for this equation: x^2 + 6x - 3 = 0
But what is the discriminant formula? And how do I use it?
I also have to determine how many real number solutions the equation has. Can you please explain how to do all this?

Answer 3

@Loser66 @TheSmartOne @Nnesha

Answer 4

Ok i can help. Is there an answer choice

Answer 5

No, I have to answer myself.

Answer 6

Use the standard form of the quadratic (ax2+bx+c) to find a,b, and c for this quadratic.
a=1,b=6,c=−3

Answer 7

do you know that right?

Answer 8

The discriminant is defined as \( \sqrt{b^2-4ac} \) which appears int he quadratic formula. If the discriminant is a real number means that the roots of the quadratic are real. So if
\[x^2 + 6x-3 = 0 \implies a = 1 \quad b = 6 \quad c = -3 \]
Then the discriminant is:
\[\sqrt{6^2 - 4(1)(-3)} = \sqrt{36+12} = \sqrt{48} \] Which is a real number

Answer 9

Let me let @kmeis002 help you lol

Answer 10

As a side note, an real quadratic equation can have 3 options. 1 real root (repeated), 2 real roots, 2 complex conjugates as roots.

If the discriminant = 0, then there will be 1 repeated root (look at the quadratic equation and it may become clear).

If the discriminant = a real number, 2 real roots occur.

If the discriminant is an imaginary number, 2 complex roots (conjugates of each other) occur.

This is why we look at the discriminant. It provides useful information about the quadratic.