Home
Class 12
MATHS
If P(x)=ax^(2)+bx+c and Q(x)=-ax^(2)+dx+...

If `P(x)=ax^(2)+bx+c` and `Q(x)=-ax^(2)+dx+c` where `ac!=0` then `P(x)Q(x)=0` has atleast

A

at least three real roots

B

no real root

C

at least two real roots

D

two real and two imaginary roots.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos
  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |5 Videos

Similar Questions

Explore conceptually related problems

If P(x)=ax^2+bx+c , Q(x)=-ax^2+dx+c where ac!=0 then P(x).Q(x)=0 has

If P(x) = ax^(2) + bx + c , and Q(x) = -ax^(2) + dx + c, ax ne 0 then prove that P(x), Q(x) =0 has atleast two real roots.

Let a, b, c in R with a gt 0 such that the equation ax^(2) + bcx + b^(3) + c^(3) - 4abc = 0 has non-real roots. If P(x) = ax^(2) + bx + c and Q(x) = ax^(2) + cx + b , then (a) P(x) gt 0 for all x in R and Q(x) lt 0 for all x in R . (b) P(x) lt 0 for all x in R and Q(x) gt 0 for all x in R . (c) neither P(x) gt 0 for all x in R nor Q(x) gt 0 for all x in R . (d) exactly one of P(x) or Q(x) is positive for all real 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) .

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

If p(x)=ax^(2)+bx and q(x)=lx^(2)+mx+n with p(1)=q(1), p(2)-q(2)=1 , and p(3)-q(3)=4 , then p(4)-q(4) is equal to

Let f(x)=ax^(2)+bx+c , g(x)=ax^(2)+px+q , where a , b , c , q , p in R and b ne p . If their discriminants are equal and f(x)=g(x) has a root alpha , then

If f(x) = a + bx + cx^(2) where c > 0 and b^(2) - 4ac < 0 . Then the area enclosed by the coordinate axes,the line x = 2 and the curve y = f(x) is given by

Consider two quadratic expressions f(x) =ax^2+ bx + c and g (x)=ax^2+px+c,( a, b, c, p,q in R, b != p) such that their discriminants are equal. If f(x)= g(x) has a root x = alpha , then

Given P(x) =x^(4) +ax^(3) +bx^(2) +cx +d such that x=0 is the only real root of P'(x) =0 . If P(-1) lt P(1), then in the interval [-1,1]

RESONANCE ENGLISH-DPP-QUESTION
  1. If alpha and beta are the roots of equation x^(2)-4x+13=0, then quadra...

    Text Solution

    |

  2. The number of integral values of 'm' less than 50, so that the roots o...

    Text Solution

    |

  3. If P(x)=ax^(2)+bx+c and Q(x)=-ax^(2)+dx+c where ac!=0 then P(x)Q(x)=0 ...

    Text Solution

    |

  4. If alpha,beta are the roots of the equation ax^2 + bx+c=0 then the roo...

    Text Solution

    |

  5. If ""(alpha)and (beta) are the roots of equation x^(2)-3x+1=0and a(n)=...

    Text Solution

    |

  6. A quadratic equation f(x)=a x^2+b x+c=0 has positive distinct roots re...

    Text Solution

    |

  7. All the values of ' a ' for which the quadratic expression a x^2+(a-2)...

    Text Solution

    |

  8. If x^(2)+ax+10=0and x^(2)+bx-10=0 have common root, then a^(2)-b^(2) i...

    Text Solution

    |

  9. The least integral value of ' a ' for which the graphs y=2a x+1 and y=...

    Text Solution

    |

  10. If the quadratic equation alpha x^2 +beta x+a^2+b^2+c^2-ab-bc-ca=0 has...

    Text Solution

    |

  11. Let x=sqrt(3-sqrt5) and y=sqrt(3+sqrt5) If the value of the expression...

    Text Solution

    |

  12. If a gt b gt 0 are two real numbers, the value of, sqrt(ab+(a-b)sqrt(...

    Text Solution

    |

  13. Consider the equation log(5)[(2+sqrt5)^(x)+(sqrt5-2)^(x)]=1/2-log(1//5...

    Text Solution

    |

  14. lf sum of maximum and minimum value of y = log2(x^4+x^2+1) - log2 (x^4...

    Text Solution

    |

  15. Find the sum of all the real solution (s) to the equation (x+y)^(2)=(x...

    Text Solution

    |

  16. If x^2 + 2(a-1)x + a + 5 = 0 has real roots belonging to the interval ...

    Text Solution

    |

  17. lf alpha and beta are the roots of the equation x^2-ax + b = 0 and ...

    Text Solution

    |

  18. Let r ,s ,a n dt be the roots of equation 8x^2+1001 x+2008=0. Then fin...

    Text Solution

    |

  19. The set of all values of ' a ' for which the quadratic equation 3x^2+2...

    Text Solution

    |

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

    Text Solution

    |