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You are watching: Factor x 4 13x 2 36



The job is to:

Find the roots of x^4 – 13x^2 + 36 = 0

We have the right to make the equation look at friendlier by letting x^2=y.

Then the equation becomes:

y^2 - 13y + 36 = 0

keeping in mind to achieve the number 13 from addition of factors of 36,...


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The task is to:

Find the roots of x^4 – 13x^2 + 36 = 0

We have the right to make the equation look friendlier by letting x^2=y.

Then the equation becomes:

y^2 - 13y + 36 = 0

Keeping in mental to acquire the number 13 from addition of determinants of 36, and knowing that 36 can be derived by multiply 9 and also 4, the administrate becomes:

(y-9)(y-4) = 0

Hence y=9 or 4.

That analyze to x^2=9 => x=+3 or -3

or x^2=4 => x=+2 or -2

Therefore, the roots of the equation are:

x1 = -3

x2 = -2

x3 = 2

x4 = 3

To evaluate the systems graphically, click the attach at the bottom of this answer


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Tushar Chandra
Educator due to the fact that 2010

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We have actually to find the root of x^4 – 13x^2 + 36 = 0. Together we have actually x increased to the power 4, we room going to have actually 4 roots.

Now let us see the offered equation :

x^4 – 13x^2 + 36 = 0

we see that -13 deserve to be composed as -4 – 9 so that the sum is -13 and the product is 36

=> x^4 – 4x^2 – 9x^2 + 36 = 0

=> x^2 ( x^2 – 4) – 9( x^2 – 4) = 0

=> (x^2 – 4)(x^2 – 9) =0

Now x^2 – 4 and also x^2 – 9 have the right to be factorized making use of the relationship x^2 – y^2 = (x – y)*(x + y)

=> (x – 2)(x + 2)(x – 3)(x + 3) =0

So for (x – 2) = 0, we have x = 2

for (x + 2) = 0, we have x = -2

for (x – 3) = 0 we have x = 3

and because that (x + 3) =0, we have actually x = -3

Therefore the root of x^4 – 13x^2 + 36 = 0 are x = 2, x = -2, x = 3 and also x = -3.

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