Answer:
Given the equation: \(-11x^2 = x+11\)
or we can write above equation as:
\(-11x^2-x-11=0\) or
\(11x^2+x+11 =0\)
The general equation of quadratic formula for \(ax^2+bx+c=0\); where a, b and c are constant;
Use Discriminant formula: \(D =b^2-4ac\)
If \(D> 0\), then there are 2 roots.
If D = 0, then there is only 1 root.
If D <0, then there are no real roots.
Now, from the given equation \(11x^2+x+11 =0\) we have
a =11, b= 1 and c =11
Then, using discriminant formula we have;
\(D =b^2-4ac =(1)^2 -4(11)(11) = 1-4\cdot 121 = 1-484= -483\)
⇒D<0 [ No real roots]
Therefore, for the given equation \(-11x^2 = x+11\) , there are no real solutions.
