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I. x2 + 3x - 18 = 0, II. y2 + y - 30 = 0 to solve both the equations to find the values of x and y?

Correct answer: E. If x = y or the relationship between x and y cannot be established.

  • 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

The first equation factors as (x + 6)(x - 3) = 0, giving x = -6 or 3. The second factors as (y + 6)(y - 5) = 0, giving y = -6 or 5, so x may be less than, equal to, or greater than y depending on the roots selected. Option a is a common mistake because it compares only 3 and 5 and ignores the other roots.

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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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