Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread
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anyone who can help me with question 12b and 13a of exercise 4F?
The first question:
The "sum of the products of pairs of roots" refers to the x term which is absent, meaning the coefficient is 0. Therefore the "sum of the products of pairs of roots" = 0
Algebraically: ab + a(a+b) + b(a+b) = 0 [... a = alpha, b = beta]
Expanding: ab + a^2 + ab + ab + b^2 = 0
ab + a^2 + 2ab + b^2 = 0
Combining the perfect square:
ab + (a+b)^2 = 0
And you can use the results from the question before 12a what (a+b)^2 is.
That is substitute (a+b) = 1/2*A = A/2
ab + (A/2)^2 = 0
ab + (A^2)/4 = 0
Therefore: ab = -(A^2)/4 = -1/4 * A^2
Sorry if it's hard to read. Rats i was late again...