Answer:
b. real, irrational, and unequal
Step-by-step explanation:
Roots of a quadratic equation
The standard representation of a quadratic equation is:
[tex]ax^2+bx+c=0[/tex]
where a,b, and c are constants.
Solving with the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
The argument of the radical is called the discriminant:
[tex]d=b^2-4ac[/tex]
The nature of the solutions of the equation depends on the value of d as follows:
We are given the equation:
[tex]-2x^2+6x+5=0[/tex]
Here: a=-2, b=6, c=5. The discriminant is:
[tex]d=6^2-4(-2)(5)=36+80=116[/tex]
d = 116
Since d is positive and a non-perfect square, the roots are:
b. real, irrational, and unequal
