You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Properties of Cube Root of a Complex Number

If p, q, r,...

Question

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

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

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 $5$

Suggest Corrections

Similar questions

Q. If r,s are the roots of the equation x²-px+q=0, then what is the equation of the curve whose roots are ([1/r] + s) and ([1/s]+r)?

Q. Let

p, q

be the roots of the equation

x^{2} - 2 x + A = 0

and let

r, s

be the roots of the equation

x^{2} - 18 x + B = 0.

p, q, r, s

with

p < q < r < s

are in A.P., then

Q. If p, q, r are roots of the equation

(x - 3) (x^{2} - 9 x - 2018) = 0

, then

p + q + r

is?

Q. If all the roots of the equation

p x^{4} + q x^{2} + r = 0, p \neq 0, q^{2} \geq 9 p r

are real, then which of the following option(s) is/are correct?

Match the column

$\begin{matrix} Equation & Name of the curve 1) x^{2} - 2 x - y - 3 = 0 & P) Circle 2) x^{2} + 3 x y + 2 y^{2} - x - 4 y - 6 = 0 & Q) Parabola 3) x^{2} + y^{2} - 20 = 0 & R) Ellipse 4) 7 x^{2} + 7 y^{2} + 2 x y + 10 x - 10 y + 7 = 0 & S) Hyperbola 5) 6 x^{2} - x y - y^{2} - 23 x + 4 y + 15 = 0 & T) Pair of straight lines \end{matrix}$

Join BYJU'S Learning Program

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 $5$