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I. x2 - x - 42 = 0, II. y2 - 17y + 72 = 0 to solve both the equations to find the values of x and y?

Correct answer: A. If x < y

  • A. If x < y
  • B. If x > y
  • C. If x ≤ y
  • D. If x ≥ y
  • E. If x = y or the relationship between x and y cannot be established.

Explanation

Factoring the first equation gives (x - 7)(x + 6) = 0, so x = 7 or -6. The second gives (y - 8)(y - 9) = 0, so y = 8 or 9; even the larger x-value, 7, is less than the smaller y-value, 8. The likely mistake is choosing b by comparing only the positive-looking roots incorrectly.

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About Quadratic Equations

Quadratic equations contain a squared variable and can be solved by factorisation, completing the square, the quadratic formula, or graphical reasoning. Questions cover roots, the discriminant, and the relationship between roots and coefficients, while distinguishing real and repeated roots from complex or non-real roots.

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