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Answers
Question: if a(alpha) and b(beta) are the zeroes of the polynomial 5x^2 - 4x + 10, find a polynomial whose zeroes are 1/alpha(a) and 1/beta(b)
Answer:
x^2 - (2/5)x + 1/2 or 10x^2 - 4x + 5
Step-by-step explanation:
If a and b are zeroes of 5x^2 - 4x + 10, then using the relation in zeroes and coefficiemt, we get that
Sum = a + b = - (-4/5) = 4/5
Product = ab = 10/5 = 2
If any polynomial have roots 1/a and 1/b, then
Sum of roots = 1/a + 1/b = (b + a)/ab = 2/5
Product of roots = (1/a)(1/b) = 1/ab = 1/2
Therefore, polynomial must look like,
= x^2 - (2/5)x + 1/2
If you solve it further, you get 10x^2 - 4x + 5.
Answer:
If a and b are zeroes of 5x^2 - 4x + 10, then using the relation in zeroes and coefficiemt, we get that
Sum = a + b = - (-4/5) = 4/5
Product = ab = 10/5 = 2
If any polynomial have roots 1/a and 1/b, then
Sum of roots = 1/a + 1/b = (b + a)/ab = 2/5
Product of roots = (1/a)(1/b) = 1/ab = 1/2
Therefore, polynomial must look like,
= x^2 - (2/5)x + 1/2
If you solve it further, you get 10x^2 - 4x + 5.