If the sum of the roots of the quadratic
equation is 3 and sum of their cubes is 63, find
the quadratic equation.
[3 Marks]
Answers
Answered by
12
Solution+
Let x1 and x2
==> x1+x2 = 3.......(1)
==> x1^3+ x2^3 = 63.......(2)
from (2)
==> x1^3 + x2^3 = (x1+x2)^3 - 3ab(a+b)
==> 63 = 3^3 - 3ab(3)
==> 63 = 27 - 9ab
==> 36 = -9ab
==> ab = 36/-9 = -4
Now we know that the sum = 3
and the product = -6
==> The equation is:
x^2 - 3x - 4 = 0
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