What is the discriminant of $5x^2 + 11x + 8 = 0$ and what does that mean?

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Answer 1 · 2015-07-16T19:09:13

The discriminant is -39. It tells you that there are no real roots to the equation, but there are two complex roots.

If you have a quadratic equation of the form

$ax^2+bx+c=0$

The solution is

$x = (-b±sqrt(b^2-4ac))/(2a)$

The discriminant $Δ$ is $b^2 -4ac$ .

The discriminant "discriminates" the nature of the roots.

There are three possibilities.

Your equation is

$5x^2 +11x +8 = 0$

$Δ = b^2 – 4ac = 11^2 -4×5×8 = 121 – 160 = -39$

This tells you that there are no real roots, but there are two complex roots.

We can see this if we solve the equation.

$5x^2 +11x +8 = 0$

$x = (-b±sqrt(b^2-4ac))/(2a) = (-11±sqrt(11^2 -4×5×8))/(2 ×5) = (-11±sqrt(121-160))/10 = (-11±sqrt(-39))/10 = 1/10(-11 ±isqrt39) = -1/10(11±isqrt39)$

$x = -1/10(11+isqrt39)$ and $x = -1/10(11-isqrt39)$

There are no real roots, but there are two complex roots to the equation.

What is the discriminant of 5x^2 + 11x + 8 = 05x^2 + 11x + 8 = 0 and what does that mean?