Home
Class 12
MATHS
If the quadratic polynomials defined on ...

If the quadratic polynomials defined on real coefficient
`P(x)=a_(1)x^(2)+2b_(1)x+c_(1)` and `Q(x)=a_(2)x^(2)+2b_(2)x+c_(2)` take positive values `AA x in R`, what can we say for the trinomial `g(x)=a_(1)a_(2)x^(2)+b_(1)b_(2)x+c_(1)c_(2)` ?

A

g(x) takes positive values only

B

g(x) takes positive values only

C

g(x) can take positive as well as negative values

D

nothing definite can be said about g(x)

Text Solution

Verified by Experts

The correct Answer is:
A
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 two equation a_(1) x^(2) + b_(1) x + c_(1) = 0 and, a_(2) x^(2) + b_(2) x + c_(2) = 0 have a common root, then the value of (a_(1) b_(2) - a_(2) b_(1)) (b_(1) c_(2) - b_(2) c_(1)) , is

If the lines x=a_(1)y + b_(1), z=c_(1)y +d_(1) and x=a_(2)y +b_(2), z=c_(2)y + d_(2) are perpendicular, then

Statement - 1 : For the straight lines 3x - 4y + 5 = 0 and 5x + 12 y - 1 = 0 , the equation of the bisector of the angle which contains the origin is 16 x + 2 y + 15 = 0 and it bisects the acute angle between the given lines . statement - 2 : Let the equations of two lines be a_(1) x + b_(1) y + c_(1) = 0 and a_(2) x + b_(2) y + c_(2) = 0 where c_(1) and c_(2) are positive . Then , the bisector of the angle containing the origin is given by (a_(1) x + b_(1) y + c_(1))/(sqrt(a_(2)^(2) + b_(1)^(2))) = (a_(2) x + b_(2)y + c_(2))/(sqrt(a_(2)^(2) + b_(2)^(2))) If a_(1) a_(2) + b_(1) b_(2) gt 0 , then the above bisector bisects the obtuse angle between given lines .

Find the condition for two lines a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 to be (i) parallel (ii) perpendicular

Given a_(i)^(2) + b_(i)^(2) + c_(i)^(2) = 1, i = 1, 2, 3 and a_(i) a_(j) + b_(i) b_(j) + c_(i) c_(j) = 0 (i !=j, i, j =1, 2, 3) , then the value of the determinant |(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))| , is

If (x - a) be a factor common to a_(1)x^(2) + b_(1)x +c and a_2x^2 + b_(2)x + c , then prove that: alpha(a_(1)-a_(2))=b_(2)-b_(1)

The asymptotes of the hyperbola (x^(2))/(a_(1)^(2))-(y^(2))/(b_(1)^(2))=1 and (x^(2))/(a_(2)^(2))-(y^(2))/(b_(2)^(2))=1 are perpendicular to each other. Then, (a) a_(1)/a_(2)=b_(1)/b_(2) (b) a_(1)a_(2)=b_(1)b_(2) (c) a_(1)a_(2)+b_(1)b_(2)=0 (d) a_(1)-a_(2)=b_(1)-b_(2)

Let n be positive integer such that, (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then a_(r) is :

If two circles x^(2)+y^(2)+2a_(1)x+2b_(1)y=0 and x^(2)+y^(2)+2a_(2)x+2b_(2)y=0 touches then show that a_(1)b_(2)=a_(2)b_(1)

If the expansion in power of x of the function (1)/(( 1 - ax)(1 - bx)) is a_(0) + a_(1) x + a_(2) x^(2) + a_(3) x^(3) + …, then a_(n) is

RESONANCE ENGLISH-DPP-QUESTION
  1. Sum of all the 4-digit numbers which can be formed using the digits 0,...

    Text Solution

    |

  2. If y = f(x),has following graph Match the column by filling follo...

    Text Solution

    |

  3. If the quadratic polynomials defined on real coefficient P(x)=a(1)x^...

    Text Solution

    |

  4. The exponent of 12 in 100! Is

    Text Solution

    |

  5. Number of words each consisting of two vowels and two consonants which...

    Text Solution

    |

  6. The number of zeros at the end of 70!, is

    Text Solution

    |

  7. The coefficient of x^5in(1+2x+3x^2+)^(-3//2)i s(|x|<1) 21 b. 25 c. 26...

    Text Solution

    |

  8. it is known for x ne 1 that 1+x+x^(2)+"….."+x^(n-1) = (1-x^(n))/(1-x),...

    Text Solution

    |

  9. Match the following :

    Text Solution

    |

  10. How many even numbers are there with three digits such that if 5 is...

    Text Solution

    |

  11. The number of different seven-digit numbers that can be written usin...

    Text Solution

    |

  12. Number of natural numbers between 100 & 1000 such that at least one of...

    Text Solution

    |

  13. A class consists of 4 boys and g girls. Every Sunday five students, in...

    Text Solution

    |

  14. Let A,B,C,D be collinear points in that order. Suppose AB: CD = 3:2 an...

    Text Solution

    |

  15. If A & B are the points (-3,4)a n d(2,1) , then the co-ordinates of th...

    Text Solution

    |

  16. If a triangle A B C ,A-=(1,10), circumcenter -=(-1/3,2/3), and orthoce...

    Text Solution

    |

  17. If the 6th term in the expansion of(1/(x^(8/3))+x^2(log)(10)x)^8 is 56...

    Text Solution

    |

  18. If the second term of the expansion [a^(1/(13))+a/(sqrt(a^(-1)))]^n is...

    Text Solution

    |

  19. The co-efficient of x in the expansion of (1-2x^3+3x^5)(1+1/x)^8 is:

    Text Solution

    |

  20. If (1!)^(2) + (2!)^(2) + (3!)^(2) + "…….." + (99!)^(2) is divided by 1...

    Text Solution

    |