Determine the nature of the roots of the quadratic equation without solving it. $8 x - 1 = 5 x ^ { 2 }$
A) two imaginary roots
B) one rational root
C) two irrational roots
D) two rational roots

Question

Determine the nature of the roots of the quadratic equation without solving it. $8 x - 1 = 5 x ^ { 2 }$
A) two imaginary roots
B) one rational root
C) two irrational roots
D) two rational roots

Quizplus · Accepted Answer

The equation can be written as $5x^2 - 8x + 1 = 0$, which is a quadratic equation in standard form. We can find the discriminant of the equation, which is $b^2 - 4ac = (-8)^2 - 4(5)(1) = 24$. Since the discriminant is positive but not a perfect square, the roots of the equation are two irrational roots. Therefore, the answer is (C).

Determine the Nature of the Roots of the Quadratic Equation 8x−1=5x28 x - 1 = 5 x ^ { 2 }8x−1=5x2

Determine the Nature of the Roots of the Quadratic Equation $8 x - 1 = 5 x ^ { 2 }$