# Roots questionWatch

#1
Can anyone help me on this:

Find the roots of, and factorise:

Q(x) = x^4 - x^3 - 7x^2 + x + 6

Thanks,

AK
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12 years ago
#2
(Original post by atkelly)
Find the roots of, and factorise:

Q(x) = x^4 - x^3 - 7x^2 + x + 6
0 = x^4 - x^3 - 7x^2 + x + 6

sub (x = 1) => 1^4 - 1^3 - 7 + 1 + 6 = 0, so (x-1) is a factor

division of Q(x) by (x-1) will give cubic. Try factorising this cubic. Otherwise some some values for x like above and divide by factor which is found to get quadratic. You can then use the methods to solve a quadratic to find the other two roots.
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12 years ago
#3
Q(x) = x^4 - x^3 - 7x^2 + x + 6

(x-1)(x^3-7x-6) = x^4 - x^3 - 7x^2 + x + 6

Let f(x) = x^3-7x-6
f(-1) = -1 + 7 - 6 = 0

So (x+1) is a factor

(x-1)(x+1)(x^2-x-6) = x^4 - x^3 - 7x^2 + x + 6
(x-1)(x+1)(x-3)(x+2)

x = 1
x = -1
x = 3
x = -2
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