Question

Solve x4 – 17x2 + 16 = 0. Let u = Select all of the zeroes of the function. i i

Answer 1

$Solve \ x^4 - 17x^2 + 16 = 0$

To solve this equation , we need to write it in quadratic form

$ax^2+bx+c=0$

To get the equation in quadratic form we replace x^2 with u

$x^2 = u$

$x^4 - 17x^2 + 16 = 0$ can be written as

$(x^2)^2 - 17x^2 + 16 = 0$, Replace u for x^2

So equation becomes

$u^2 - 17u + 16 = 0$

Now we factor the left hand side

-16  and -1  are the two factors whose product is +16  and sum is -17

(u-16) (u-1) = 0

u -16 = 0  so u=16

u-1 =0  so u=1

WE assume u = x^2, Now we replace u with x^2

$u = 16 so \ it \ becomes \ x^2 =16$

Now take square root on both sides , x= +4  and x=-4

$u = 1 so \ it \ becomes \ x^2 =1$

Now take square root on both sides , x= +1  and x=-1

So zeros of the function are -4, -1, 1, 4

Answer 2

Answer(s)!

(Part 1) Solve x^4-17x^2+16=0

Answer?

x^2

(Part 2) Rewrite the equation in terms u.

Answer?

u^2-17u+16=0

(Part 3) Factor

Answer?

(u-16)(u-1)=0

(Part 4) Select all of the solutions of the original equation

Answers?

x=4

x=-4

x=-1

x=1