Question

How many solutions are there for the quadratic equation?
f(x)=5x^2+3x+2

Answer 1

2

Explanation:

`5x^2 +3x +2 = 0\\\\\text{Apply the quadratic formula,}~ x=(-b \pm √(b^2 - 4ac))/(2a)\\\\\text{In this case,}~a= 5, ~ b = 3~ \text{and}~ c = 2\\\\ \\x=(-3\pm √(3^2 -4\cdot 5 \cdot 2))/(2\cdot 5)\\\\~~~=(-3 \pm √(9-40))/(10)\\\\~~~=(-3 \pm √(-31))/(10)\\\\~~~=(-3 \pm i√(31))/(10)\\\\\text{So, there are 2 solutions,}~ x=(-3 + i√(31))/(10)~ \text{and} ~x=(-3 -i√(31))/(10)`

Another way to find the number of solutions is by looking at the highest exponent(Degree), which indicates the number of solutions.

Answer 2

`\\ \rm\rightarrowtail 5x^2+3x+2=0`

`\\ \rm\rightarrowtail x=(-3\pm √(9-40))/(10)`

`\\ \rm\rightarrowtail x=(-3\pm√(-31))/(10)`

`\\ \rm\rightarrowtail x=(-3\pm√(31)i)/(10)`