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.

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.

a

step-by-step explanation: