Multiple choice

Rocky and Anthony are solving a quadratic equation. While solving, Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. Anthony commits a mistake in the coefficient of X and finds the roots to be -9 and -1. Find the correct roots.

  1. -9 and 1

  2. 9 and -1

  3. 9 and 1

  4. 8 and 1

  5. 8 and - 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rocky: roots 8, 2 => sum=10, product=16. Constant term is wrong, so sum (coefficient of x) is correct: -b/a = 10. Anthony: roots -9, -1 => sum=-10, product=9. Coefficient of x is wrong, so product (constant term) is correct: c/a = 9. Equation is x^2 - 10x + 9 = 0. Roots are (x-9)(x-1) = 0, so 9 and 1.

AI explanation

Let the correct quadratic equation be x squared plus bx plus c equals 0. Rocky found the correct sum of roots to be 8 plus 2 equals 10, so b equals -10. Anthony found the correct product of roots to be -9 multiplied by -1 equals 9, so c equals 9. The correct equation is x squared minus 10x plus 9 equals 0, which factors to (x - 9)(x - 1) equals 0. Therefore, the correct roots are 9 and 1.

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