The number of times the graph of f(x) where a≠ 0 can come in contact with x- axis is? f(x)=ax3+bx2+cx+d
Answers
Answer:
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Answer: A cubic equation has the form
ax3 + bx2 + cx + d = 0
It must have the term in x
3 or it would not be cubic (and so a 6= 0), but any or all of b, c and d
can be zero. For instance,
x
3 − 6x
2 + 11x − 6 = 0, 4x
3 + 57 = 0, x3 + 9x = 0
are all cubic equations.
Just as a quadratic equation may have two real roots, so a cubic equation has possibly three.
But unlike a quadratic equation which may have no real solution, a cubic equation always has at
least one real root. We will see why this is the case later. If a cubic does have three roots, two
or even all three of them may be repeated. This gives us four possibilities which are illustrated
in the following examples.
Example
Suppose we wish to solve the equation
x
3 − 6x
2 + 11x − 6 = 0
This equation can be factorised to give
(x − 1)(x − 2)(x − 3) = 0
This equation has three real roots, all different - the solutions are x = 1, x = 2 and x = 3.
In Figure 1 we show the graph of y = x
3 − 6x
2 + 11x − 6.
Step-by-step explanation: If it's hrlp full then please mark me as good.
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