Question

is one root of quadratic equation 2x2 + x + 1 = 0, find k.​

Answer 1

Answer:

$\large\boxed{x=-\frac{1}{5}=-0.2 }$

Step-by-step explanation:

To find the value of k,  first you have to use the quadratic equation of 2x2+x+1=0. Isolate by the x on one side of the equation from left to right.

Given:

2x*2+x+1=0

Solutions:

To use quadratic equation formula:

$\large\boxed{\textnormal{Quadratic Equations}}$

$\displaystyle x=\frac{-b+\sqrt{b^2-4ac} }{2a}$

First, you have to multiply numbers from left to right.

$\displaystyle 2*2=4$

$\displaystyle 4x+x+1=0$

Add.

$\displaystyle 4x+x=5x$

$\displaystyle 5x+1=0$

Secondly, subtract 1 from both sides.

$\displaystyle 5x+1-1=0-1$

Solve.

$\displaystyle 0-1=-1$

$\displaystyle 5x=-1$

Then, divide by 5 from both sides.

$\displaystyle \frac{5x}{5}=\frac{-1}{5}$

Change into a fraction.

$\large\boxed{x=-\frac{1}{5}}$

Divide.

$\displaystyle1\div5=\boxed{-0.2}$

Therefore, the final answer is x=-1/5=-0.2

Answer 2

${\huge {\boxed{\bold{\boxed{\mathfrak{\color{red}{Answer}}}}}}}$

Given quadratic equation: 2x^2 + x + 1 = 0

Now, compare the given quadratic equation with the general form ax^2 + bx + c = 0

On comparing, we get

a = 2, b = 1 and c = 1

Therefore, the discriminant of the equation is:

D = b^2– 4ac

Now, substitute the values in the above formula

D = (1)^2 – 4(2)(1)

D = 1- 8

D = -7

Therefore, the required solution for the given quadratic equation is

x =[-b ± √D]/2a

x = [-1 ± √-7]/2(2)

We know that, √-1 = i

x = [-1 ± √7i] / 4

Hence, the solution for the given quadratic equation is (-1 ± √7i) / 4

Hope it's Helpful....:)