Pandalover5165 Pandalover5165
  • 22-10-2019
  • Mathematics
contestada

For what value of k are there two complex solutions to the given quadratic equation (k+1)x²+4kx+2=0.

Respuesta :

nuuk nuuk
  • 22-10-2019

Answer:[tex]k\in \left ( \frac{-1}{2},1\right )[/tex]

Step-by-step explanation:

Given

[tex]\left ( k+1\right )x^2+4kx+2=0[/tex]

For complex  roots Discriminant should be zero

D<0

[tex]D=\sqrt{b^2-4ac}[/tex]

here

[tex]D=\sqrt{\left ( 4k\right )^2-4\left ( k+1\right )\left ( 2\right )}[/tex]

[tex]D=\sqrt{16k^2-8k-8}<0[/tex]

so [tex]16k^2-8k-8<0[/tex]

[tex]2k^2-k-1<0[/tex]

[tex]\left ( 2k+1\right )\left ( k-1\right )<0[/tex]

so [tex]k\in \left ( \frac{-1}{2},1\right )[/tex]

Answer Link

Otras preguntas

¡Hola, soy Berta! Mis amigas y yo vivimos en un apartamento cerca de la universidad.Somos buenas amigas, pero (1) ___ actividades muy diferentes.Por la mañana,
what should be added to 3x³-5x²+7x-4 to get 7x³+2x²-3x+9​
What sources of data are used by demographers?
What is the maximum weight a girl can lose in 30 days?
The denominator of a fraction exceeds numerator by 3. If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the ori
If xn = (n−1)cos(n2 +n+1) 2n−1 EXERCISES then xn has a convergence subsequence.
Two factors that decide the success of any structural system are what?
What are good films on martial arts and courage for my media studied
PLEAZE HELP IM STUCK PLS
Why would an object have a much lower maximum speed falling through water than falling through air?​