Question

find the value of k if x=1/√3 is a root of the quadratic equation: kx²+(√3-√2)x-1=0​

Answer 1

Answer:

2.448

Step-by-step explanation:

Given that, x = 1/root3 is a root of the quadratic equation: kx2 + (root3-root2)x - 1 =0

now, substitute x value in given equation .

the answer is in above picture.

Answer 2

Answer:

√6

Step-by-step explanation:

Concept= Quadratic Equation

Given = The quadratic equation

To find= The value of k

Explanation=

We have been the question as find the value of k if x=1/√3 is a root of the quadratic equation: kx²+(√3-√2)x-1=0​

Since we know that when we solve a quadratic equation ax² +bx +c=0, we get some values of x. This x is the root of the quadratic equation. So if we put the values of x in the quadratic equation the equation satisfies that result is 0.

So we know that x= 1/√3 is the root of the given quadratic equation  

kx²+(√3-√2)x-1=0​

Putting the value of x=1/√3 in the equation and solving it further we get,

kx²+(√3-√2)x-1=0​

=> k(1/√3)² + (√3 - √2)*1/√3 - 1 =0

=> k/3 + (√3/√3 - √2/√3) - 1 = 0

=> k/3 + 1 - √2/√3 - 1 = 0

=> k/3 -√2/√3 = 0

=> k/3 = √2/√3

=> k = 3*√2/√3

=> k= √3*√2

=> k = √(3*2)

=> k= √6

Therefore we find that the value of k is √6.

#SPJ2