if equation x^3 -3x^2+mx+k has three real roots, then which of the following cannot be true?
A. m=0,k=2
B. m=1,k=1
C. m=-3,k=3
D. m=4,k=-12
Answers
answer : option (D) m = 4 , k = -12
explanation : if we choose m = 4, k = -12
equation converts into , x³ - 3x² + 4x - 12 = 0
now, let's resolve it
= x³ - 3x² + 4x - 12
= x²(x - 3) + 4(x - 3)
= (x² + 4)(x - 3)
here we see , expression breaks only into two factors. (x - 3) and (x² + 4)
we know, x² + 4 ≠ 0 for all real value of x.
hence, when we put m = 4 and k = -12, it has only one real root i.e., 3
so, option (D) m = 4 and k = -12 , is correct choice.
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Answer:
D. M=4,k=-12
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