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Let x^3+ax^2+bx+c be the given cubic pol...

Let `x^3+ax^2+bx+c` be the given cubic polynomlal and
f(x) = 0 be the corresponding cubic equation, where a,b,c, `in` R
Now,`f^'(x)=3x^2+2ax+b`
Let `D=4a^2-12b=4(a^2-3b)` be the discriminant of the equation f(x)=0 then
If `D=4(a^2-3b)gt0` and `f(x_1,).f(x_2)gt0`.
where `x_1,x_2` are the roots of f'(x),then

A

a) f(x) has all real and disitinct roots

B

b) f(x)would have three real roots but one of the would be
repacted

C

c) f(x)would have just one real root

D

d) none of the above

Text Solution

Verified by Experts

The correct Answer is:
C
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PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
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