Home
Class 12
MATHS
Statement -1 : one root of the equation ...

Statement -1 : one root of the equation `x^(2)+5x-7=0` lie in the interval (1,2).
and
Statement -2 : For a polynomial f(x),if f(p)f(q) lt 0, then there exists at least one real root of f(x) =0 in (p,q)

A

Statement -1 is True, Statement -2 is True, Statement -2 is a correct explanation for statement -13

B

Statement -1 is True, Statement -2 is True , Statement -2 is NOT a correct explanation for Statement -13

C

Statement -1 is True, Statement -2 is False

D

Statement -1 is Flase, Statement -2 is True

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Section-F ( Matrix -Match type Question)|7 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise section-G( Integer Answer type Questions)|8 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -D) Linked comprehension Type Questions|14 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (section-J) Objective type question (Aakash Challengers Questions)|4 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos

Similar Questions

Explore conceptually related problems

Statement -1: f(x) = x^(3)-3x+1 =0 has one root in the interval [-2,2]. Statement-2: f(-2) and f(2) are of opposite sign.

Let a and b be two distinct roots of a polynomial equation f(x) =0 Then there exist at least one root lying between a and b of the polynomial equation

Statement-1: If a, b, c in R and 2a + 3b + 6c = 0 , then the equation ax^(2) + bx + c = 0 has at least one real root in (0, 1). Statement-2: If f(x) is a polynomial which assumes both positive and negative values, then it has at least one real root.

If one the roots fo the equation x^(2) +x f(a) + a=0 is the cube of the othere for all x in R , then f(x)=

Statement-1: If alpha and beta are real roots of the quadratic equations ax^(2) + bx + c = 0 and -ax^(2) + bx + c = 0 , then (a)/(2) x^(2) + bx + c = 0 has a real root between alpha and beta Statement-2: If f(x) is a real polynomial and x_(1), x_(2) in R such that f(x_(1)) f_(x_(2)) lt 0 , then f(x) = 0 has at leat one real root between x_(1) and x_(2) .

Statement-1: The equation e^(x-1) +x-2=0 has only one real root. Statement-2 : Between any two root of an equation f(x)=0 there is a root of its derivative f'(x)=0

Let f(x) be a quadratic polynomial satisfying f(2) + f(4) = 0. If unity is one root of f(x) = 0 then find the other root.

If for all real values of a one root of the equation x^2-3ax + f(a)=0 is double of the other, then f(x) is equal to

Statement-1: If a, b, c, A, B, C are real numbers such that a lt b lt c , then f(x) = (x-a)(x-b)(x-c) -A^(2)(x-a)-B^(2)(x-b)-C^(2)(x-c) has exactly one real root. Statement-2: If f(x) is a real polynomical and x_(1), x_(2) in R such that f(x_(1)) f(x_(2)) lt 0 , then f(x) has at least one real root between x_(1) and x_(2)

Statement 1: If 27 a+9b+3c+d=0, then the equation f(x)=4a x^3+3b x^2+2c x+d=0 has at least one real root lying between (0,3)dot Statement 2: If f(x) is continuous in [a,b], derivable in (a , b) such that f(a)=f(b), then there exists at least one point c in (a , b) such that f^(prime)(c)=0.

AAKASH INSTITUTE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assertion -Reason Type Questions
  1. Statement-1 : let z(1) and z(2) be two complex numbers such that arg ...

    Text Solution

    |

  2. Statement-1 : The locus of z , if arg((z-1)/(z+1)) = pi/2 is a circ...

    Text Solution

    |

  3. Statement-1 : If e^(itheta)=cos theta +isintheta and the value of e...

    Text Solution

    |

  4. Statement-1 : z(1)^(2) + z(2)^(2) +z(3)^(2) +z(4)^(2) =0 " where " z(1...

    Text Solution

    |

  5. Statement -1 : For any four complex numbers z(1),z(2),z(3) and z(4) ,...

    Text Solution

    |

  6. Statement -1 : The expression ((2i)/(1+i))^(n) is a positive integer ...

    Text Solution

    |

  7. Statement -1 : if 1-i,1+i, z(1) and z(2) are the vertices of a square...

    Text Solution

    |

  8. Statement-1 : IF |z+1/z| =a , where z is a complex number and a is a ...

    Text Solution

    |

  9. Statement-1 : The locus of complex number z, satisfying (z-2)^(n) =z^...

    Text Solution

    |

  10. Statement -1 : A root of the equation (2^(10)-3)x^(2)-2^(11)x +2^(10)+...

    Text Solution

    |

  11. Statement -1: The equation who roots are reciprocal of the roots of th...

    Text Solution

    |

  12. Statement-1 : The equation x^(2)-2009x+2008 =0 has rational roots . ...

    Text Solution

    |

  13. Statement -1 : one root of the equation x^(2)+5x-7=0 lie in the interv...

    Text Solution

    |

  14. Statement -1 : The quadratic equation ax^(2)+bx+c=0 has real roots if...

    Text Solution

    |

  15. Statement -1 : There is just on quadratic equation with real coefficie...

    Text Solution

    |

  16. Statement -1 : The roots of x^(2) +2sqrt(2008)x +501=0 are irrational...

    Text Solution

    |

  17. Statement -1 : if a,b,c not all equal and a ne 0 ,a^(3) +b^(3) +c^(3)...

    Text Solution

    |

  18. Statement -1 : There is just one quadratic equation with real coeffici...

    Text Solution

    |

  19. Statement-1 : Let a quadratic equation has a root 3 - 9i then the sum...

    Text Solution

    |