Multiple choice

If $p$ and $q$ are the roots of the equation $x^2-30x+221=0$, what is the value of $p^3+q^3$ ?

  1. $7010$
  2. $7110$
  3. $7210$
  4. $7240$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For x^2 - 30x + 221 = 0, p+q = 30 and pq = 221. p^3 + q^3 = (p+q)(p^2 - pq + q^2) = (p+q)((p+q)^2 - 3pq) = 30 * (30^2 - 3*221) = 30 * (900 - 663) = 30 * 237 = 7110.

AI explanation

Using Vieta's formulas, the sum of the roots p + q is 30 and the product pq is 221. The sum of cubes identity states p^3 + q^3 = (p + q)^3 - 3pq(p + q). Substituting the known values gives 30^3 - 3(221)(30), which evaluates to 27000 - 19890 = 7110.

Keep practicing — related questions