Question

Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=5x^2–7x+12.

Answer 1

Consider the general case

`ax^2+bx+c=0`

This equation has the solutions

`x=\frac{-b\text{ }\pm\sqrt[]{b^2-4ac}}{2a}`

In here, the quantity

`b^2-4ac`

is called the discriminant. If the discriminant is greater than or equal to zero, then the roots of the equation are real. If the discriminant is negative, the roots are imaginary (complex roots).

In our case 5x^2-7x+12, a=5,b=-7,c=12. Then, the discrimininant is

`b^2-4ac=(-7)^2-4\cdot5\cdot12\text{ = 49-240 = -191<0}`

This means that the roots of this equation are all imaginary (complex).