These questions are pertaining to Applied Calculus

Question

Calculate the discriminant for the following equation and describe the nature of its roots

 

                                                         3x^2-7x -6=0

 

Δ = ______________________

 

a) The equation has two irrational roots

b) The equation has two rational roots

c) The equation has one rational root

d) The equation has no real roots

 

 

Answer 1

From Algebra II courses we learn that discriminant (a.k.a. 'delta') is b² - 4ac.

 

If discriminant is negative, both roots are imaginary.

If discriminant is zero, there's one "double" root.

If discriminant is positive but not a perfect square, there are two irrational roots.

If discriminant is positive but delta is a perfect square (and a,b,c) are rational, then the equation has two rational roots (rational includes integers).