Find the sum of all the roots of the equation $x^{8} - 17 x^{4} + 16 = 0$ .

Open in App

Solution

Substitute $x^{4} = y$ in the equation. The equation can be written as
$y^{2} - 17 y + 16 = 0$
$∴ y_{1} = 1$ and $y_{2} = 16$ $\Rightarrow {\begin{matrix} x^{4} = 1 x^{4} = 16 \end{matrix}$
We find that $x_{1} = - 1, x_{2} = 1, x_{3} = - 2, x_{4} = 2$ .
So, the sum of all the roots $= - 1 + 1 + 2 - 2 = 0$ .

Suggest Corrections

Similar questions

Q. Sum of all the roots of the equation

x^{2} - 2 x + | x - 1 | - 5 = 0

Q. The sum of roots of the equation

x^{8} = 1

whose real part is positive is

Q. Solve the equation

{64.9}^{x} - 84. 12^{x} + 27. 16^{x} = 0

find the sum of roots.

if 1, $α_{1}$ , $α_{2}$ , $α_{3}$ ................ $α_{7}$ are the roots of the equation $x^{8}$ - 1 = 0.Find of the value of $\sum_{i = 1}^{7} (α_{i})^{2}$

Q. If the sum of two roots of the equation

4 x^{4} - 8 x^{3} - 13 x^{2} + 2 x + 3 = 0

is zero, find largest of all of its roots ?

Join BYJU'S Learning Program

Find the sum of all the roots of the equation x8−17x4+16=0.

Substitute x4=y in the equation. The equation can be written asy2−17y+16=0∴y1=1 and y2=16 ⇒{x4=1x4=16We find that x1=−1,x2=1,x3=−2,x4=2.So, the sum of all the roots =−1+1+2−2=0.

Find the sum of all the roots of the equation $x^{8} - 17 x^{4} + 16 = 0$ .