Multiple choice

Rakesh and Amit solve an equation. While solving, Rakesh commits a mistake in the constant term and finds the roots 8 and 2. Amit commits a mistake in the coefficient of X and finds the roots - 9 and - 1. Find the correct roots.

    • 8, 2

  2. 9, - 1

  3. 9, 1

  4. 8, 1

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rakesh got roots 8 and 2 (sum 10, product 16). He erred in constant term, so sum 10 is correct (coefficient of x is -10). Amit got roots -9 and -1 (sum -10, product 9). He erred in coefficient of x, so product 9 is correct. Equation is x^2 - 10x + 9 = 0. Roots are 9 and 1.

AI explanation

For a quadratic equation, the sum of the roots gives the correct coefficient of x with the opposite sign, while the product of the roots gives the correct constant term. Rakesh found the roots 8 and 2, so the correct sum of the roots is 8 + 2 = 10. Amit found the roots -9 and -1, so the correct product of the roots is (-9) * (-1) = 9. The correct quadratic equation is therefore x^2 - 10x + 9 = 0, which factors into (x - 9)(x - 1) = 0. The correct roots are 9, 1.

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