It is known that x1 and x2 are roots of the equation 6x2+7x+k=0, where 2x1+3x2=-4.

Find k.

1

Step-by-step explanation:

For a quadratic equation, the roots are expressed by the quadratic formula.

x = (-b+ / - Sqrt[b^2-4ac]) / 2a

In this case a=6, b=-7 and c=k

So,

x = (7 + / - √[ (-7) ^2-4 (6) (k) ]/2 (6))

Simplifying gives:

x = (7 + / - √[49-24k]) / 12

For k=0 the square root simplifies to √[49]=7 which yields roots of 7/6 and 0

For k=1 the square root simplifies to √[49-24]=√[25]=5 which yields roots of 1 and 1/6

For k=2 the square root simplifies to √[49-48]=√[1]=1 which yields roots of 2/3 and 1/2

k = 1 as other roots are fractions