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Find the square of (2x+3y)...

Find the square of `(2x+3y)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `y=ax^(3)+bx+c`
`:.(dy)/(dx)=3ax^(2)+b`
For maximum or minimum `(dy)/(dx)=0` we get
`x=+-sqrt(-b/(3a))`
Case If `a gt0, bgt0` then `(dy)/(dx)gt0`
In this case function is increasing so it has exactly one root
Case II If `alt0, blt0` ten `(dy)/(dx)lt0`
In this case function is decreasing so it has exactly one root.
Case III `agt0, blt0` or `alo0, bgt0` then `y=ax^(3)+bx+c` is maximum at one point and minimum at other point.
Hence all roots can never be non -netative.
`:.` Statement -1 is false. But ltgtbrgt Sum of roots `=-("Coefficient of" x^(2))/("Coefficient of"x^(3))=0`
i.e. Statement -2 is true.
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