Home
Class 11
MATHS
about to only mathematics...

about to only mathematics

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True.

Text Solution

Verified by Experts

The correct Answer is:
A
Statement-2 is the algebraic interpretation of Rolle's Theorem. So, it is true.
Let `f(x) = ax^(3) + bx^(2) + cx`. Then, `f(0) = 0 and f(1) = a + b + c = 0`.
So, 0 and 1 are roots of f(x) = 0. Therefore, by statement-2, f'(x) = 0 i.e. `3ax^(2) + 2bx + c = 0` has a root between 0 and 1.
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|138 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|123 Videos

  • PROBABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|45 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|59 Videos

Similar Questions

Explore conceptually related problems

In a certain collage, the ratio of mathematics majors to English majors is 3:8. If in the following school year the number of mathematics majors increase 20%, and the number of English majors decrease 15%, what is the new ratio of mathematics majors to English majors?

STATEMENT-1 : Magnetic poles are only mathematical assumptions and have no real existence . and STATEMENT-2 : Magnetic field lines are always in closed loops .

72% of 25 students are good in mathematics. How many are not good in mathematics?

in a class of 35 students , 17 have taken Mathematics , 10 have taken mathematics but not economics if each student has taken erither mathematics Of Economics or both , then the number of students who have taken Economics but not mathematics is

Rahim obtained 60 marks out of 75 in Mathematics. Find the percentage of marks obtained by Rahim in Mathematics.

There are five books on Mathematics and 6 books on Physics in a book shop. In how many ways can a student buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?

A bag contains a total of 20 books on physics and mathematics. Ten books are chosen from the bag and it is found that it contains 6 books of mathematics. Find out the probability that the remaining books in the bag contains 2 books on mathematics.

From 50 students taking examinations in mathematics, physics and chemistry,37 passed mathematics, 24 physics and 43 chemistry. At most 19 passed mathematics and physics, at most 29 mathematics and chemistry and at most 20 physics and chemistry. Find the largest possible number that could have passed all three exams.

From 50 students taking examinations in mathematics, physics and chemistry,37 passed mathematics, 24 physics and 43 chemistry. At most 19 passed mathematics and physics, at most 29 mathematics and chemistry and at most 20 physics and chemistry. Find the largest possible number that could have passed all three exams.

check whether it is statement or not .Do you like mathematics ?

OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Section II - Assertion Reason Type
  1. If alpha and beta are the roots of the equation x^(2)-ax+b=0and A(n)=a...

    Text Solution

    |

  2. Statement-1: If alpha and beta are real roots of the quadratic equatio...

    Text Solution

    |

  3. Statement-1: If a, b, c, A, B, C are real numbers such that a lt b lt ...

    Text Solution

    |

  4. Statement I: x^2-5x+6<0 if 2 < x < 3 Statement II: If alpha and beta, ...

    Text Solution

    |

  5. about to only mathematics

    Text Solution

    |

  6. Statement-1: There is a value of k for which the equation x^(3) - 3x +...

    Text Solution

    |

  7. Statement-1: If x^(2) + ax + 4 gt 0 "for all" x in R, then a in (-4, 4...

    Text Solution

    |

  8. If the roots of the equation ax^2 + bx + c = 0, a != 0 (a, b, c are re...

    Text Solution

    |

  9. Statement (1) : If a and b are integers and roots of x^2 + ax + b = 0 ...

    Text Solution

    |

  10. Statement-1: If a, b, c are distinct real numbers, then a((x-b)(x-c))/...

    Text Solution

    |

  11. Let f(x)=a x^2+bx +c a ,b ,c in R. If f(x) takes real values for re...

    Text Solution

    |

  12. Statement-1: If a, b, c in R and 2a + 3b + 6c = 0, then the equation a...

    Text Solution

    |

  13. Statement-1: If a ne 0 and the equation ax^(2) + bx + c = 0 has two ro...

    Text Solution

    |

  14. Statement-1: If a, b, c in Q and 2^(1//3) is a root of ax^(2) + bx + c...

    Text Solution

    |

  15. Statement-1: If f(x) = 1 + x + (x^(2))/(2!) + (x^(3))/(3!) + (x^(4))/(...

    Text Solution

    |

  16. Given that for all real x, the expression (x^(2)-2x+4)/(x^(2)+2x+4) l...

    Text Solution

    |

  17. Let a, b, c be real numbers such that ax^(2) + bx + c = 0 and x^(2) + ...

    Text Solution

    |

  18. Statement-1: The cubic equation 4x^(3) - 15x^(2)+14x-5 = 0 has a root ...

    Text Solution

    |

  19. Statement-1: The equation (pi^(e))/(x-e)+(e^(pi))/(x-pi)+(pi^(pi)+e^(e...

    Text Solution

    |

  20. Consider a quadratic equation ax^(2) + bx + c = 0, where 2a + 3b + 6c ...

    Text Solution

    |