find the following :

Question

Given the equation 4x^2+5x-6=0

what is value of the discriminant? 

How many solutions are there and what type? (Ex:1,imaginary) 

find the solutions using quadratic formula 

Answer 1

Aisha

 

Some of the information you need is in the answer to the question involving x^2+6x+c=0.

 

Again the discriminant is b² -4ac

 

In your equation 4x^2+5x-6=0   a = 4, b = 5 and c = -6.

 

When we plug those values into the discriminant we get

 

     5² - 4(4)(-6) = 25 + 256 = 281

 

Since this is greater than 0 so there are 2 real solutions. To decide if the solutions are rational or irrational we look at the value of the discriminant.  If it is a perfect square then they are rational.  If not a perfect square then irrational.

 

This problem would have 2 real irrational solutions

 

Quadratic formula   x=(-b±sqrt(b^2-4ac))/(2a)   Now plug the values for a, b, and c into the formula 

 

      x=(-b+/-sqrt(b^2-4ac))/(2a). 

 

      x=(-5 ± sqrt(5^{2 -} 4(4)(-6))/2(4)

 

     x = (-5± sqrt(25 + 256))8

 

     x = -5 ± sqrt(281)/8    Since sqrt 218 is not a perfect square the two solutions are real and irrational.