Question

What is the discriminate of the equation 2x+5x^2=1?

Answer 1

Answer:

24

Step-by-step explanation:

First we must recognize that this equation is a quadratic function, therefore we can use the quadratic equation and look only at the discriminate portion of that formula.  However, before doing so we need to set up our equation by taking the 1 to the other side and so:

$2x+5x^2=1\\\\5x^2+2x-1=0$

And we know that in general a quadratic function is such that:

$ax^2+bx+c$

And so our quadratic equation is:

$\frac{-b \pm \sqrt{b^2-4ac} }{2a}$

But we only need to look at what's under the square root meaning:

$b^2-4ac$

This is our discriminant and since a=5, b=2 and c=-1  we have:

$b^2-4ac=(2^2)-4(5)(-1)=24$