Determine the nature of the roots of the quadratic equation without solving it. $3 x ^ { 2 } + 8 = x$
A) two rational roots
B) one rational root
C) two irrational roots
D) two imaginary roots

Question

Determine the nature of the roots of the quadratic equation without solving it. $3 x ^ { 2 } + 8 = x$
A) two rational roots
B) one rational root
C) two irrational roots
D) two imaginary roots

Quizplus · Accepted Answer

We can rewrite the equation in standard quadratic form as $3x^2-x+8=0$. Using the discriminant ($b^2-4ac$) of the quadratic formula, we find that it is negative: $(-1)^2-4(3)(8)=-95<0$. This means that the quadratic has two complex (imaginary) roots.

Determine the Nature of the Roots of the Quadratic Equation 3x2+8=x3 x ^ { 2 } + 8 = x3x2+8=x

Determine the Nature of the Roots of the Quadratic Equation $3 x ^ { 2 } + 8 = x$