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thanks, and another question

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.
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Replies, comments and Discussions:

  • 工作学习 / 求学深造 / a math question thanks!! Suppose triangle ABC has side lengths a, b, c, Prove that if a*a+b*b+c*c=ab+bc+ac, then triangle ABC is an equilateral triangle.
    • in
      a*a+b*b>=2*a*b;
      b*b+c*c>=2*b*c;
      c*c+a*a>=2*c*a;
      each = is true only if x==y


      2(a*a+b*b+c*c)>=2(a*b+b*c+c*d)

      the = is true only if
      a==b==c
    • thanks, and another question
      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.
      • n*n*n-n*n-4 =(n-2)*(n*n+n+2)
      • Why do you do such easy questions? n*n*n-n*n-4=(n-2)(n*n+n+2), so it is a composite number.
    • (a-b)**2+(b-c)**2+(c-a)**2=0
      这可是基本功啊!!
    • 2(a*a+b*b+c*c)=2*(ab+ba+ac) > (a-b)^2 + (b-c)^2+(a-c)^2=0 >a=b,b=c,a=c
    • too easy. a*a+b*b+c*c if and only if a=b=c>0, no matter a b c are the sides of a triangle or not.
    • 你在上几年级?