If $p, q, r, s, t$ are the roots of the equation $x^{5} - 1 = 0$ , then $p^{10} + q^{10} + r^{10} + s^{10} + t^{10} =$

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Solution

The correct option is C $5$
$p, q, r, s, t$ are all fifth root of unity
$\Rightarrow p^{5} = q^{5} = r^{5} = s^{5} = t^{5} = 1$
$\Rightarrow p^{10} = q^{10} = r^{10} = s^{10} = t^{10} = 1$
Hence, the required sum is $5$

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If p,q,r,s,t are the roots of the equation x5−1=0, then p10+q10+r10+s10+t10=

The correct option is C 5p,q,r,s,t are all fifth root of unity⇒p5=q5=r5=s5=t5=1 ⇒p10=q10=r10=s10=t10=1Hence, the required sum is 5

If $p, q, r, s, t$ are the roots of the equation $x^{5} - 1 = 0$ , then $p^{10} + q^{10} + r^{10} + s^{10} + t^{10} =$

The correct option is C $5$
$p, q, r, s, t$ are all fifth root of unity
$\Rightarrow p^{5} = q^{5} = r^{5} = s^{5} = t^{5} = 1$
$\Rightarrow p^{10} = q^{10} = r^{10} = s^{10} = t^{10} = 1$
Hence, the required sum is $5$