Determine the nature of the roots of the quadratic equation without solving it. $x ^ { 2 } + 5 = x$
A) two imaginary roots
B) two rational roots
C) one rational root
D) two irrational roots

Question

Determine the nature of the roots of the quadratic equation without solving it. $x ^ { 2 } + 5 = x$
A) two imaginary roots
B) two rational roots
C) one rational root
D) two irrational roots

Quizplus · Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. For the given equation $x^2 - x + 5 = 0$, the discriminant is $(-1)^2 - 4(1)(5) = 1 - 20 = -19$, which is less than 0. This indicates the equation has two imaginary roots.

Determine the Nature of the Roots of the Quadratic Equation x2+5=xx ^ { 2 } + 5 = xx2+5=x

Determine the Nature of the Roots of the Quadratic Equation $x ^ { 2 } + 5 = x$