Solving Equation

Question

The equation 4x² +kx+9=0 has exactly one root.

For the value(s) of k, find the root or roots.

Answer 1

The discriminant of Ax²+Bx+C = 0 is B² - 4AC.

 

If the discriminant is zero, then Ax²+Bx+C has only one root.  

 

So, if 4x²+kx+9 = 0 has only one root, then k² - 4(4)(9) = 0

 

                                                                             k² = 144

 

                                                                             k = ±12

 

If k = 12, then 4x² + kx + 9 = (2x+3)² = 0 when x = -3/2.

 

If k = -12, then 4x² + kx + 9 = (2x-3)² = 0 when x = 3/2.

  

Answer 2

factor: (2x + 3) (2x + 3) = 0

k = 12

x = -3/2