write the equation y+2/y = -1 in standard form and write the value of a,b,c
multiply all terms by y
y^2 + 2 = -y
add y to both sides
y^2 + y + 2 = 0
a y^2 + b y + c = 0
a = 1
b = 1
c = 2
To write the equation \(y + \frac{2}{y} = -1\) in standard form, we need to eliminate the fraction. To do this, let's start by multiplying every term in the equation by \(y\) to get rid of the denominator:
\(y \cdot y + \frac{2}{\cancel{y}} \cdot \cancel{y} = -1 \cdot y\)
This simplifies to:
\(y^2 + 2 = -y\)
Next, let's bring all the terms to one side of the equation to obtain the standard form:
\(y^2 + y + 2 = 0\)
So, the equation \(y + \frac{2}{y} = -1\) in standard form is \(y^2 + y + 2 = 0\).
In the standard form equation \(ay^2 + by + c = 0\), the values of \(a\), \(b\), and \(c\) can be identified as follows:
\(a = 1\), as the coefficient of the \(y^2\) term is 1.
\(b = 1\), as the coefficient of the \(y\) term is 1.
\(c = 2\), as the constant term is 2.
Therefore, the values of \(a\), \(b\), and \(c\) for the equation \(y^2 + y + 2 = 0\) are \(a = 1\), \(b = 1\), and \(c = 2\).