If the teacher says, "describe the nature of the roots" what does she mean?

Question

the equation is 2x^2-7x-4=0

There are two real distinct roots, I'm just not sure why

I know there's a chart of some kind telling when to use 1 or 2 real or imaginary roots, I just can't remeber it. Thanks

Answer 1

In order to find the nature of the roots, you need to look at the discriminant. The discriminant is the square root (b^2-4ac) of the quadratic formula.

If the discriminant is less than zero, there are two complex, imaginary roots.

If the discriminant is equal to zero, there are two equal real rational roots. Since they are equal, some interpret it as one root.

If the discriminant is greater than zero and a perfect square (4, 9, 16, 25...), there are two real rational roots.

If the discriminant is greater than zero but not a perfect square, there are two real irrational roots.

Going back to your equation:

D = (square root)(-7^2 - 4(2)(-4)
D = (square root)(49 + 32)
D = (square root)(81)

81 is a perfect square. Therefore, the roots are two real rational roots.

Answer 2

Nature Of The Roots

Answer 3

Your so-called "chart" is called a discriminant, and is the middle part of the quadratic formula : √(b^2-4ac). If this resolves to a positive number, you have two real roots to the equation, If this resolves to zero, you have a single root If this resolves to a negative number, you have two imaginary roots. In you example this would be √{-7^2 - (4)(2)(-4)} which simplifies to √(49 + 32), or √81, so you have two real roots.

Answer 4

This Site Might Help You.

RE:
If the teacher says, "describe the nature of the roots" what does she mean?
the equation is 2x^2-7x-4=0

There are two real distinct roots, I'm just not sure why

I know there's a chart of some kind telling when to use 1 or 2 real or imaginary roots, I just can't remeber it. Thanks

Answer 5

if the answer is zero, then the roots are double.

if the answer is positive, there are two real roots.

if the answer is negative, there are two complex roots.

does that sound right? i hope i helped.

Answer 6

What she is referring to is your Family Tree.