The number of distinct real roots of `x^4-4x^3+12 x 62+x-1=0i s________dot`
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The correct Answer is:
2
Let ` f(x) = x^(4) - 4x ^(3) + 12 x^(2) + x - 1 ` ` therefore f'(x) = 4x ^(3) - 12 x^(2) + 24 x + 1` and ` f''(x) = 12 x^(2) - 24x + 24 gt 0 ` for all real x. So, graph of f'(x) intersects x - axis only once . Hene, f(x) has only one turning point . Also `f(0) = - 1` . so, graph of f(x) cuts x-axis at two points Hence , f(x) = 0 has two real roots .
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