Multiple choice

If coefficient of x and constant term of a quadratic equation are taken wrongly roots were found to be 8, 3 and 7, 3 respectively. Find the actual roots of the equation.

  1. 12, 2

  2. 5, 2

  3. 8, 2

  4. 6, 4
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D Correct answer
Explanation

Wrong coefficient of x: roots 8, 3 => sum = 11, product = 24. Correct constant term is 24. Wrong constant term: roots 7, 3 => sum = 10, product = 21. Correct coefficient of x is -10. Equation: x^2 - 10x + 24 = 0. Roots: (x-6)(x-4) = 0 => 6, 4.

AI explanation

In a quadratic equation, the coefficient of x represents the negative sum of the roots, and the constant term represents the product of the roots. Since the coefficient of x was taken wrongly to give roots of 8 and 3, their sum of 11 is wrong, but their correct product is 3 multiplied by 8, which is 24. Similarly, since the constant term was taken wrongly to give roots of 7 and 3, their product of 21 is wrong, but their correct sum is 7 plus 3, which is 10. We now find two numbers whose sum is 10 and product is 24, which are 6 and 4, making them the actual roots.

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