Multiple choice

What is the sum of the square of the roots of the equation p² - 13p + 9 = 0 ?

  1. 169

  2. 162

  3. 151

  4. 154

  5. 144
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C Correct answer
Explanation

For p^2 - 13p + 9 = 0, sum of roots (r1+r2) = 13, product (r1*r2) = 9. Sum of squares = r1^2 + r2^2 = (r1+r2)^2 - 2(r1*r2) = 13^2 - 2(9) = 169 - 18 = 151.

AI explanation

Using the relationship between roots and coefficients for the equation p squared minus 13p plus 9 equals zero, the sum of the roots is 13 and the product is 9. The sum of the squares of the roots is found using the identity sum squared minus twice the product. Substituting the values gives 169 minus 18, which equals 151.

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