Question

The square of (2x - 3y)
​

Answer 1

Answer:

Solution

Let

y=ax^(3)+bx+c

<br>

:.(dy)/(dx)=3ax^(2)+b

<br> For maximum or minimum

(dy)/(dx)=0

we get <br>

x=+-sqrt(-b/(3a))

<br> Case If

a gt0, bgt0

then

(dy)/(dx)gt0

<br> In this case function is increasing so it has exactly one root <br> Case II If

alt0, blt0

ten

(dy)/(dx)lt0

<br> In this case function is decreasing so it has exactly one root. <br> Case III

agt0, blt0

or

alo0, bgt0

then

y=ax^(3)+bx+c

is maximum at one point and minimum at other point. <br> Hence all roots can never be non -netative. <br>

:.

Statement -1 is false. But ltgtbrgt Sum of roots

=-("Coefficient of" x^(2))/("Coefficient of"x^(3))=0

<br> i.e. Statement -2 is true.