There are two parts in this question.
a) Prove that if a quadratic equation has consective integers as its coefficients, then it has no real roots.
B), Prove or disprove the theorem that if a quadratic equation has three consecutive integers as its coefficients, then it has no real roots.
Well, I did the second part as :
the quadratic equation (n-1)x*x+nx+(n+1)=0, where n>=2.
then b*b-4ac<0,
it is true.
What should I write the first part? How to tell them apart?
Thanks again.
the third question is ' Prove that f(n)=n*n*n-n*n-4 is a composite number. (ie, not a prime number) for all integers n>2.
a) Prove that if a quadratic equation has consective integers as its coefficients, then it has no real roots.
B), Prove or disprove the theorem that if a quadratic equation has three consecutive integers as its coefficients, then it has no real roots.
Well, I did the second part as :
the quadratic equation (n-1)x*x+nx+(n+1)=0, where n>=2.
then b*b-4ac<0,
it is true.
What should I write the first part? How to tell them apart?
Thanks again.
the third question is ' Prove that f(n)=n*n*n-n*n-4 is a composite number. (ie, not a prime number) for all integers n>2.