Question

What are the roots to the quadratic equation with the following coefficients in standard form?

a=2, b=-3, c=-4


Given the following constants for a standard form quadratic equation, determine the nature of its roots.

a=3, b=3, c=2

Answer 1

\[x=\frac{ -\left( -3 \right)\pm \sqrt{\left( -3 \right)^{2}-4*2*-4} }{ 2*2 }\]
\[x=\frac{ 3\pm \sqrt{9+32} }{4 }=\frac{ 3\pm \sqrt{41} }{4 }\]

Answer 2

For the second part of the question:

\[a = 3, b = 3, c = 2\rightarrow 3x^2+3x+2=0\]

The nature of the roots is given by examining the discriminant, which is \(b^2-4ac\):

if \(b^2-4ac =0\) the radical disappears entirely, and the equation has 1 unique root whose value is \(-b/2a\)

if \(b^2-4ac >0\) there will be two real roots

if \(b^2-4ac < 0\) there will be a conjugate pair of complex roots