Answer:
Answer= real, equal, rational.
Step-by-step explanation:
[tex]4x^{2} +48x+144=0[/tex]
a=4
b=48
c=144
- To determine the nature of the roots use the formula [tex]b^{2} -4ac[/tex].
[tex]b^{2} -4ac[/tex]
[tex]=48^{2} -4*4*144[/tex]
=0
If [tex]b^{2} -4ac=0[/tex] that means the roots are real, equal and rational.
EXTRA INFORMATION:
- If [tex]b^{2} -4ac>0[/tex] and it was also a perfect square that means the roots are real, distinct and rational.
- If [tex]b^{2} -4ac>0[/tex] and it was also not a perfect square that means the roots are real, distinct and irrational.
- If [tex]b^{2} -4ac<0[/tex] that means the roots are imaginary.
- If [tex]b^{2} -4ac\geq 0[/tex] that means the roots are real.
