Multiple choice

lf roots of the equation $\mathrm{x}^{2}-$ bx $+\mathrm{c}=0$ be two consectutive integers, then $\mathrm{b}^{2}-4\mathrm{c}$ equals

  1. $-2$
  2. $3$
  3. $2$
  4. $1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If roots are n and n+1, then sum = 2n+1 = b and product = n(n+1) = c. b^2 - 4c = (2n+1)^2 - 4(n^2+n) = 4n^2 + 4n + 1 - 4n^2 - 4n = 1.

AI explanation

Let the two consecutive integers be n and n+1, so by Vieta's formulas b = n + (n+1) = 2n+1 and c = n(n+1) = n^2+n. Substituting these into the expression gives (2n+1)^2 - 4(n^2+n) = 4n^2+4n+1 - 4n^2-4n = 1.

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