SOF International Mathematics Olympiad (IMO)
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Set B
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2025
.
Sample
Find the roots of the quadratic equation x² + (10)x + (24) = 0.
Explanation
Explanation
We need two numbers whose sum is -10 and product is 24 (since for x² + bx + c, sum of roots = -b, product = c). Those numbers are -4 and -6, so the equation factors as (x - (-4))(x - (-6)) = 0, giving x = -4 or x = -6.
PRO TIP
Re-check your working by substituting the answer back into the original question.
If the sum of the roots of a quadratic equation is -1 and the product of the roots is -6, what is the equation (in the form x² - (sum)x + (product) = 0)?