Multiple choice

In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains $-9$ and $-1$ for the roots. Another student makes a mistake in the constant term of the equation and obtains $8$ and $2$ for the roots. The correct equation was?

  1. $x^2+10x+9=0$
  2. $x^2-10x+16=0$
  3. $x^2-10x+9=0$

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First student (mistake in linear coefficient): Roots -9, -1. Product = 9. Correct constant term is 9. Second student (mistake in constant term): Roots 8, 2. Sum = 10. Correct linear coefficient is -10. Equation: x^2 - 10x + 9 = 0.

AI explanation

The standard form of a quadratic equation is x squared minus the sum of the roots times x plus the product of the roots. The first student obtained the correct constant term but incorrect first degree coefficient, giving a correct product of the roots as negative 9 times negative 1, which equals 9. The second student obtained the correct first degree coefficient but incorrect constant term, giving a correct sum of the roots as 8 plus 2, which equals 10. Combining these correct values, the correct equation is x squared minus 10 x plus 9 equals 0.

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