JEE Exam  >  JEE Questions  >  Given p ( x ) = x 4 + ax3 + bx 2 + cx + d suc... Start Learning for Free
Given p ( x ) = x 4 + ax3 + bx 2 + cx + d such that x =0 is the only real root of p ' ( x ) = 0 .
 If p ( -1) < p (1) , then in the interval [-1,1]
  • a)
    p ( -1) is the minimum and p (1) is the maximum of P
  • b)
     p ( -1) is not minimum but p (1) is the maximum of P
  • c)
    p ( -1) is the minimum and p (1) is not the maximum of P
  • d)
    neither p ( -1) is the minimum nor p (1) is the maximum of P
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Given p ( x ) = x 4 + ax3 + bx 2 + cx + d such that x =0 is the only r...
p ' (x ) has only one change of sign. x = 0 is a point of minima.
P(-1) =1- a + b + d P(0) = d
P(1) =1+ a + b + d
P ( -1) < P (1) , P ( 0) < P (1) , P ( -1) > P ( 0)
P (-1) is not minimum but P(1) is maximum
View all questions of this test
Most Upvoted Answer
Given p ( x ) = x 4 + ax3 + bx 2 + cx + d such that x =0 is the only r...
Since x = 0 is the only real root of p(x) = 0, this means that p(x) does not have any other real roots. Therefore, the imaginary roots must come in conjugate pairs.

If x = 0 is a root of p(x) = 0, then p(0) = 0. This means that d = 0.

We are given that p(-1) = 0. Plugging in x = -1 into p(x), we get:

p(-1) = (-1)^4a + (-1)^3b + (-1)^2c + (-1)d = a - b + c

Since p(-1) = 0, we have:

a - b + c = 0

We also know that x = 0 is a root, so plugging in x = 0 into p(x), we get:

p(0) = (0)^4a + (0)^3b + (0)^2c + (0)d = 0

Since d = 0, we have:

0 = 0

This equation is always true, so it does not provide any additional information.

Therefore, the equation a - b + c = 0 is the only equation we have to work with. With this equation and the given information, we cannot determine the values of a, b, and c.
Explore Courses for JEE exam
Given p ( x ) = x 4 + ax3 + bx 2 + cx + d such that x =0 is the only real root of p ' ( x ) = 0 .If p ( -1) < p (1) , then in the interval [-1,1]a)p ( -1) is the minimum and p (1) is the maximum of Pb)p ( -1) is not minimum but p (1) is the maximum of Pc)p ( -1) is the minimum and p (1) is not the maximum of Pd)neither p ( -1) is the minimum nor p (1) is the maximum of PCorrect answer is option 'B'. Can you explain this answer?
Question Description
Given p ( x ) = x 4 + ax3 + bx 2 + cx + d such that x =0 is the only real root of p ' ( x ) = 0 .If p ( -1) < p (1) , then in the interval [-1,1]a)p ( -1) is the minimum and p (1) is the maximum of Pb)p ( -1) is not minimum but p (1) is the maximum of Pc)p ( -1) is the minimum and p (1) is not the maximum of Pd)neither p ( -1) is the minimum nor p (1) is the maximum of PCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Given p ( x ) = x 4 + ax3 + bx 2 + cx + d such that x =0 is the only real root of p ' ( x ) = 0 .If p ( -1) < p (1) , then in the interval [-1,1]a)p ( -1) is the minimum and p (1) is the maximum of Pb)p ( -1) is not minimum but p (1) is the maximum of Pc)p ( -1) is the minimum and p (1) is not the maximum of Pd)neither p ( -1) is the minimum nor p (1) is the maximum of PCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given p ( x ) = x 4 + ax3 + bx 2 + cx + d such that x =0 is the only real root of p ' ( x ) = 0 .If p ( -1) < p (1) , then in the interval [-1,1]a)p ( -1) is the minimum and p (1) is the maximum of Pb)p ( -1) is not minimum but p (1) is the maximum of Pc)p ( -1) is the minimum and p (1) is not the maximum of Pd)neither p ( -1) is the minimum nor p (1) is the maximum of PCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Given p ( x ) = x 4 + ax3 + bx 2 + cx + d such that x =0 is the only real root of p ' ( x ) = 0 .If p ( -1) < p (1) , then in the interval [-1,1]a)p ( -1) is the minimum and p (1) is the maximum of Pb)p ( -1) is not minimum but p (1) is the maximum of Pc)p ( -1) is the minimum and p (1) is not the maximum of Pd)neither p ( -1) is the minimum nor p (1) is the maximum of PCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Given p ( x ) = x 4 + ax3 + bx 2 + cx + d such that x =0 is the only real root of p ' ( x ) = 0 .If p ( -1) < p (1) , then in the interval [-1,1]a)p ( -1) is the minimum and p (1) is the maximum of Pb)p ( -1) is not minimum but p (1) is the maximum of Pc)p ( -1) is the minimum and p (1) is not the maximum of Pd)neither p ( -1) is the minimum nor p (1) is the maximum of PCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Given p ( x ) = x 4 + ax3 + bx 2 + cx + d such that x =0 is the only real root of p ' ( x ) = 0 .If p ( -1) < p (1) , then in the interval [-1,1]a)p ( -1) is the minimum and p (1) is the maximum of Pb)p ( -1) is not minimum but p (1) is the maximum of Pc)p ( -1) is the minimum and p (1) is not the maximum of Pd)neither p ( -1) is the minimum nor p (1) is the maximum of PCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Given p ( x ) = x 4 + ax3 + bx 2 + cx + d such that x =0 is the only real root of p ' ( x ) = 0 .If p ( -1) < p (1) , then in the interval [-1,1]a)p ( -1) is the minimum and p (1) is the maximum of Pb)p ( -1) is not minimum but p (1) is the maximum of Pc)p ( -1) is the minimum and p (1) is not the maximum of Pd)neither p ( -1) is the minimum nor p (1) is the maximum of PCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Given p ( x ) = x 4 + ax3 + bx 2 + cx + d such that x =0 is the only real root of p ' ( x ) = 0 .If p ( -1) < p (1) , then in the interval [-1,1]a)p ( -1) is the minimum and p (1) is the maximum of Pb)p ( -1) is not minimum but p (1) is the maximum of Pc)p ( -1) is the minimum and p (1) is not the maximum of Pd)neither p ( -1) is the minimum nor p (1) is the maximum of PCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Given p ( x ) = x 4 + ax3 + bx 2 + cx + d such that x =0 is the only real root of p ' ( x ) = 0 .If p ( -1) < p (1) , then in the interval [-1,1]a)p ( -1) is the minimum and p (1) is the maximum of Pb)p ( -1) is not minimum but p (1) is the maximum of Pc)p ( -1) is the minimum and p (1) is not the maximum of Pd)neither p ( -1) is the minimum nor p (1) is the maximum of PCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev