27. The number of positive integral values of x that
satisfy x^3 - 32x - 5x² + 64 = 0 is/are
Answers
Answer:
Case 1: All three roots are real; (Graph might touch/cut the x-axis once, twice or thrice.)
In this case depending on the equality or inequality of the roots we might have the following cases:
Case (i) All three roots are equal; (The graph of the function would intersect the X-axis only once as all the three roots of the equation coincide.)
Case (ii) Two roots are equal and one root is distinct; (In this case the graph cuts the X-axis at one point and touches the X-Axis at another point where the other two roots coincide.)
Case (iii) All three roots are distinct from each other. (In this case the graph of the function cuts the x-axis at three distinct points.)
Case 2: One root is real and two roots are imaginary. (Graph would cut the X-axis only once.)
The shapes of the graph that a cubic function can take has already been discussed as a part of the discussion on the Back to School write up of this block.
Step-by-step explanation:
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