Question

A,b,c belongs to r consider the quadratic equation ax^2+bx+c=0 has imaginary roots the a+b+1 has sign

Answer 1

Answer:

Step-by-step explanation:

To say that the roots of

ax2+bx+c=0

are imaginary is to say that the graph of:

f(x)=ax2+bx+c

does not intersect the x

axis for any real value of x .

Since this is described as a quadratic, we must have

a≠0

.

So the whole of the parabola either lies on one side of the

x

axis or the other.

When we multiply by

a≠0 ,

getting a2x2+abx+ac

whose graph is simply a scaled version of the original, the coefficient of

x2 is a2>0

. Hence we know that for large values of

x

the quadratic function will be positive. Hence it is positive for all values of x

Hope it helps you....