Multiple choice

If a, b and c are the roots of the cubic equation x3 - 7x2 + 14x - 8 = 0, then find the value of a2 + b2 + c2.

  1. 7

  2. 14

  3. 18

  4. 21

  5. 28
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For x^3 - 7x^2 + 14x - 8 = 0, sum of roots a+b+c = 7, sum of roots taken two at a time ab+bc+ca = 14. We need a^2+b^2+c^2 = (a+b+c)^2 - 2(ab+bc+ca) = 7^2 - 2(14) = 49 - 28 = 21.

AI explanation

Using the relationship between roots and coefficients for a cubic equation, we identify the sum of the roots as a + b + c = 7 and the sum of their pairwise products as ab + bc + ca = 14. We then use the algebraic identity a^2 + b^2 + c^2 = (a + b + c)^2 - 2(ab + bc + ca). Substituting the values gives 7^2 - 2(14) = 49 - 28 = 21. The value of a^2 + b^2 + c^2 is 21.

Keep practicing — related questions