For the following implication pose a key question answer the

For the following implication, pose a key question, answer the question abstractly, and apply your answer to the specific problem: \"If d is an integer >2, then the equation x^2 + 3x + d = 0 has no real solution.\"

Solution

1)

For what values of b and c does the following quadratic have real solutions?

x^2+bx+c=0

2)

Discriminant is given by:

D=b^2-4c

We ahve real solution if and only if D>=0

3)

IN given problem b=3

So setting D>=0 gives

3^2-4d>=0 for real solutions

Let, d=2.1>2

D=3^2-2.1*4=8-8.4=0.6>0 hence for d=2.1>2 we have a real solution

Hence given statement in 3) is incorrect