Home
Class 12
MATHS
If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,...

If `f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c` ,where ac`!=0,` then prove that `f(x)g(x)=0` has at least two real roots.

A

At least three real roots

B

No real roots

C

At least two real roots

D

At most two imaginary roots

Text Solution

Verified by Experts

The correct Answer is:
C, D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

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

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assertion -Reason Type Questions|19 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -B) (objective Type Questions ( one option is correct)|78 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

If b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one real root.

If f(x)=x^2+x+3/4 and g(x)=x^2+a x+1 be two real functions, then the range of a for which g(f(x))=0 has no real solution is (A) (-oo,-2) (B) (-2,2) (C) (-2,oo) (D) (2,oo)

Let f (x) =ax ^(2) +bx + c,a ne 0, such the f (-1-x)=f (-1+ x) AA x in R. Also given that f (x) =0 has no real roots and 4a + b gt 0. Let p =b-4a, q=2a +b, then pq is:

Let f(x) = x2 + b_1x + c_1. g(x) = x^2 + b_2x + c_2 . Real roots of f(x) = 0 be alpha, beta and real roots of g(x) = 0 be alpha+gamma, beta+gamma . Least values of f(x) be - 1/4 Least value of g(x) occurs at x=7/2

Let f(x) = x2 + b_1x + c_1. g(x) = x^2 + b_2x + c_2 . Real roots of f(x) = 0 be alpha, beta and real roots of g(x) = 0 be alpha+gamma, beta+gamma . Least values of f(x) be - 1/4 Least value of g(x) occurs at x=7/2

If f(x)=x^3+b x^2+c x+d and f(0),f(-1) are odd integers, prove that f(x)=0 cannot have all integral roots.

Let f(x)=x^(2)+bx+c and g(x)=x^(2)+b_(1)x+c_(1) Let the real roots of f(x)=0 be alpha, beta and real roots of g(x)=0 be alpha +k, beta+k fro same constant k . The least value fo f(x) is -1/4 and least value of g(x) occurs at x=7/2 The roots of g(x)=0 are

If the equation a x^2+b x+c=x has no real roots, then the equation a(a x^2+b x+c)^2+b(a x^2+b x+c)+c=x will have a. four real roots b. no real root c. at least two least roots d. none of these

If a+b+c=0(a,b, c are real), then prove that equation (b-x)^2-4(a-x)(c-x)=0 has real roots and the roots will not be equal unless a=b=c .

Let f(x)=ax^(2)+bx+c , g(x)=ax^(2)+qx+r , where a , b , c , q , r in R and a lt 0 . If alpha , beta are the roots of f(x)=0 and alpha+delta , beta+delta are the roots of g(x)=0 , then

AAKASH INSTITUTE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -C) (objective Type Questions ( more thena one options are correct )
  1. The pressure-volume of various thermodynamic process is shown in graph...

    Text Solution

    |

  2. If z(1) ,z(2) be two complex numbers satisfying the equation |(z(1)...

    Text Solution

    |

  3. If sin alpha, cosalpha are the roots of the equation x^2 + bx + c = 0 ...

    Text Solution

    |

  4. If alpha, beta are the roots of the equation ax^(2) +2bx +c =0 and a...

    Text Solution

    |

  5. The solution set of the inequality (x+3)^(5) -(x -1)^(5) ge 244 is

    Text Solution

    |

  6. Let a,b,c be real numbers in G.P. such that a and c are positive , the...

    Text Solution

    |

  7. Let cos alpha be a root of the equation 25x^(2) +5x -12 = 0 -1 lt x...

    Text Solution

    |

  8. If the quadratic equations x^(2) +pqx +r=0 and z^(2) +prx +q=0 have a...

    Text Solution

    |

  9. The quadratic equation x^(2) - (m -3)x + m =0 has

    Text Solution

    |

  10. If both roots of the equation x^(2) -2ax+a^(2)-1=0 lie between -3 and...

    Text Solution

    |

  11. Let alpha, beta " the roots of " x^(2) -4x + A =0 and gamma, delta " ...

    Text Solution

    |

  12. For the equation x^(3/4(logx)^(2)+log(2)x-5/4)=sqrt2, which one of the...

    Text Solution

    |

  13. If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,where ac!=0, then prove that f...

    Text Solution

    |

  14. Sum of the squares of all integral values of a for which the inequalit...

    Text Solution

    |

  15. If the roots of the equation 1/(x+p) + 1/(x+q) = 1/r are equal in mag...

    Text Solution

    |

  16. Find the integral values of a for which (a+2)x^2+2(a+1)x+a=0 will have...

    Text Solution

    |

  17. If (x-1)^(2) is a factor of ax^(3) +bx^(2) +c then roots of the equa...

    Text Solution

    |

  18. If b^(2)ge4ac for the equation ax^(4)+bx^(2)+c=0 then all the roots of...

    Text Solution

    |

  19. If the difference between the roots of the equation x^2+a x+1=0 is les...

    Text Solution

    |

  20. The set of all real numbers a such that a^2+2a ,2a+3,a n da^2+3a+8 are...

    Text Solution

    |