Multiple choice

In the equation ${x^2-7x+2=0}$, the sum of the roots exceeds the product of the roots by

  1. $9$
  2. $5$
  3. $.9$
  4. $-5$
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B Correct answer
Explanation

Sum of roots = 7. Product of roots = 2. Difference = 7 - 2 = 5.

AI explanation

For the standard quadratic equation ax^2 + bx + c = 0, Vieta's formulas state that the sum of the roots is -b/a and the product of the roots is c/a. In the given equation x^2 - 7x + 2 = 0, the values are a = 1, b = -7 and c = 2. The sum of the roots is -(-7)/1 = 7 and the product of the roots is 2/1 = 2. The difference between the sum and the product is 7 - 2, which equals 5.

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