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

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6 years ago

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```										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 & RegardsJitender SinghIIT DelhiaskIITians Faculty
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2 years ago

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