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Grade 12Differential Calculus

show that the equation x4+4x3-4x-13=0 has two real roots and two imaginary roots.


Profile image of sohan singh singh
16 Years agoGrade 12
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1 Answer

Profile image of Jitender Singh
11 Years ago
Ans:
f(x) = x^{4} +4x^{3}-4x-13 = 0
f(1) = 1^{4} +4.1^{3}-4.1-13 = -12
f(2) = 2^{4} +4.2^{3}-4.2-13 = 27
→There is one root lie b/w (1, 2)
f(-3) = (-3)^{4} +4.(-3)^{3}-4.(-3)-13 = -28
f(-4) = (-4)^{4} +4.(-4)^{3}-4.(-4)-13 = 3
→There is another root lie b/w (3, 4) which is close to 4.
-> There is no other inteval like this in which f(x) changes its sign.
-> So the other two roots are imaginary.
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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