if a,b are the zeroes of p(x)=ax2+bx+c,then find 1/a2+1/b2

Asked by FEHMEEDAH NAZNEEN | 31st Aug, 2010, 09:10: AM

Expert Answer:

Please make sure the coefficients a and b are the roots of the quadratic equation,
p(x) = ax2+bx+c
Since a and b are the roots, we can write by substituing for x, a and b respectively,
a3 + ab + c = 0    ....(1)
ab2 + b2 + c = 0  ...(2)
Also (x - a)(x - b) = 0
x2 - (a+b) + ab = 0
Comparing with given p(x),
b/a = -a - b
c/a = ab
c = a2b
We can use this c in (1) and (2), to get the desired result. But unless the form of answer is specified, it can be in terms of a,b and c.

Answered by  | 31st Aug, 2010, 09:42: AM

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