Find the discrimant b^2-4ac. Do the following quadratic equations have two distinct real solutions, a single solution, or no real solutions? 2x^2+9x=3

Question

 Asks for the number of solutons

Answer 1

Student,

 

When you get a problem like this, always express the quadratic equation in standard form

 

ax² + bx + c,

 

so you can read off a, b, and c.  Then evaluate the discriminant

 

D = b² - 4ac.

 

There are exactly 3 possibilities:

 

D > 0 ⇒ 2 different real roots, rational if D is a perfect square, irrational otherwise

D = 0 ⇒ 1 root of multiplicity 2, which means the quadratic expression is itself a perfect square

D < 0 ⇒ 2 complex roots, where one is the complex conjugate of the other

Answer 2

A=2 B=9 C=-3

 

 

B^2 - 4 A C = 81 - 4(2)(-3)

                     = 81 - -24

                    = 105

 

    Since 105 is not a perfect square, the solutions are IRRATIONAL.

   There shall be 2 distinct Real (but irrational) solutions