Question

If p and q are the zeroes of the polynomial x² + x + 1 , then find the value of 1p+1q

and
p^2+q^2
urgent.
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Answer 1

Answer:

If p & q are zeroes of x² + x + 1

Then, p + q = -1

and pq = 1

1)

$\frac{1}{p} + \frac{1}{q} = \frac{p + q}{pq} = \frac{ - 1}{1} = - 1$

2)

WE KNOW THAT,

${p}^{2} + {q}^{2} = {(p + q)}^{2} - 2pq$

SO,

${p}^{2} + {q}^{2} = { ( - 1)}^{2} + {(1)}^{2} - 2(1) = 2$ - 2 = 0

CONCLUSION:

So,

$\frac{1}{p} + \frac{1}{q} = - 1$

&

p² + q² = 0