Question

Consider the quadratic equation: 5x2 + 2x + 1 = 0. 1) Which statement is true about the roots of the given quadratic equation? A) 1 real root of multiplicity 2 B) 2 distinct real roots C) 1 complex root and 1 real root Eliminate D) 2 complex roots

Answer 1

Hello!

In math, there is always something called the discriminant. This is represented by the equation $b^{2} -4ac$, when a quadratic = $ax^{2} + bx + c$. The discriminant tells you what roots an equation has. A discriminant of over 0 represents 2 real roots, a discriminant of 0 = 1 real root, and a discriminant of <0 is 0 real roots (2 complex roots)

Now, substitute in the values and solve. In this equation, a = 5, b = 2, c = 1.

$b^{2} -4ac$

$2^{2} -4(5)(1)$

$4 - 20$

$-16$

Therefore, the discriminant is -16. This means that the equation has no real roots, and has 2 complex roots. Therefore, your answer is D.

Hope this helps!