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Answer:
1. Sometimes
2. Sometimes
3. Always
4. Sometimes
Step-by-step explanation:
1. Quadratic function : in which maximum power of is two.
The roots of quadratic function can be either equal or different.
For example:
will have two equal roots i.e. 1 and 1.
will have two different roots i.e. 1 and 2.
So, <em>sometimes </em>is the correct answer.
2. Cubic function has atleast 1 real root.
Cubic function has maximum power of as 3.
If the coefficients are real numbers then atleast 1 real root.
If the coefficients are imaginary in nature, then this is not true.
For example:
Cubic equation does not have any real root.
Cubic equation has a real root x = -1.
So, it is sometimes true.
3. A function with degree 5 i.e. maximum power of as 5 will have 5 roots.
It is always true that a function will have number of roots equal to its degree.
4. Quadratic function can have only 1 complex solution.
Two complex solutions are also possible for a quadratic function.
For example:
will have two imaginary roots:
It is also possible to have 1 complex solution,
For example:
will have one complex root and one real root.
So, the statement is <em>sometimes </em>true.