It is known that x and y are roots of the equation , where .
Find k

Step-by-step explanation:

We have the quadratic equation:

Where x and y are the roots of the equation and:

First, using the quadratic formula with a = 6, b = 7, and c = k, we can find the roots to be:

Simplify:

So, our two roots are:

For our first root, we can multiply both sides by 2.

And for our second root, we can multiply both sides by 3.

So, this produces:

Since we are given that:

By substitution:

Remove the fractions by multiplying both sides by 12:

Combine like terms:

Adding 35 to both sides produces:

So:

Squaring produces:

Therefore:

Step-by-step explanation:

We are going to express

y in terms of x.

=> 2x + 3y = -4, y = (-4 - 2x)/3.

By Vieta's Formula,

We have SOR = -b/a and POR = c/a.

=> x + y = -7/6, xy = k/6.

When x + y = -7/6,

x + (-4 - 2x)/3 = -7/6.

=> (x - 4)/3 = -7/6

=> (x - 4) = -7/2

=> x = 4 - 7/2

=> x = 0.5.

When xy = k/6,

x(-4 - 2x)/3 = k/6.

Hence k = 6[x(-4 - 2x)/3]

= 2x(-4 - 2x) = 2(0.5)(-4 - 2(0.5)) = -5.

The value of k is -5.

2/3

step-by-step explanation:

i think the answer is true

step-by-step explanation: