The equation
has a pair of equal roots. All its roots are,
X^4 +9x^3+12x^2 – 80x-192 = 0
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0
Answer:
Given equation, x
4
+9x
3
+12x
2
−80x−192=0
Consider f(x)=x
4
+9x
3
+12x
2
−80x−192
∴f’(x)=4x
3
+27x
2
+24x−80
Now, HCF of f(x) and f’(x) is (x+4). Hence −4 is atleast a double root of f(x)=0
f(x) can be factored as (x+4)
2
(x
2
+x−12)or(x+4)
3
(x−3)
∴ Roots of the given equation are −4,−4,−4,3
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0
Answer:
Hlo friend
who is nithish so intelligent to solve such a long question
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