Which number, when multiplied by
another number greater than it by 3,
gives a product 12 short of 100.
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Answer:
Explanation:
x + x = x*x
then 2x = x²
then x = x²/2
then 0 = x²/2 - x
which is a model of the quadratic polynomial y = ax² + bx + c
where a = 1/2, b = -1 and c = 0
we compute the discriminant delta (D)
recall: D = b² - 4ac
then D = (-1)² - 4*(1/2)*0 = 1 – 0 = 1
D is positive (=1) then 2 solutions (x and x’)
recall: x = -b + SQRT(D) and x' = -b - SQRT(D)
then x = -(-1) + SQRT(1) = 1 + 1 = 2
then x' = -(-1) - SQRT(1) = -1 - 1 = 0
conclusion:
• what is (are) the number(s) when multiplied or added to itself (themselves), give(s) the same result?
• answer: 0 and 2
:-))
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