Home
Class 11
MATHS
If a0, a1, a2, a3 are all the positive,...

If `a_0, a_1, a_2, a_3` are all the positive, then `4a_0x^3+3a_1x^2+2a_2x+a_3=0` has least one root in `(-1,0)` if (a) `a_0+a_2=a_1+a_3 ` and `4a_0+2a_2>3a_1+a_3` (b) `4a_0+2a_2<3a_1+a_3` (c) `4a_0+2a_2=3a_1+a_0`and `4a_0+a_2lta_1+a_3` (d) none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos
  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

If (a_2a_3)/(a_1a_4) = (a_2+a_3)/(a_1+a_4)=3 ((a_2 -a_3)/(a_1-a_4)) then a_1,a_2, a_3 , a_4 are in :

Let a_1,a_2,a_3…… ,a_n be in G.P such that 3a_1+7a_2 +3a_3-4a_5=0 Then common ratio of G.P can be

cIf a_1,a_2,a_3,..,a_n in R then (x-a_1)^2+(x-a_2)^2+....+(x-a_n)^2 assumes its least value at x=

If a_0,a_1,a_2,.... be the coefficients in the expansion of (1+x+x^2)^n in ascending powers of x. prove that : (i) a_0a_1-a_1a_2+a_2a_3-....=0

If a_1,a_2,a_3,a_4 are in HP , then 1/(a_1a_4)sum_(r=1)^3a_r a_(r+1) is root of :

If a_1,a_2 ...a_n are nth roots of unity then 1/(1-a_1) +1/(1-a_2)+1/(1-a_3)..+1/(1-a_n) is equal to

Evaluate: /_\ |[1+a_1, a_2, a_3],[a_1, 1+a_2, a_3],[a_1, a_2, 1+a_3]|

Evaluate: /_\ |[1+a_1, a_2, a_3],[a_1, 1+a_2, a_3],[a_1, a_2, 1+a_3]|

If a_1, a_2, a_3,.....a_n are in H.P. and a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1 a_n , then k is equal to

The equation A/(x-a_1)+A_2/(x-a_2)+A_3/(x-a_3)=0 ,where A_1,A_2,A_3gt0 and a_1lta_2lta_3 has two real roots lying in the invervals. (A) (a_1,a_2) and (a_2,a_3) (B) (-oo,a_1) and (a_3,oo) (C) (A_1,A_3) and (A_2,A_3) (D) none of these

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If |z-(1/z)|=1, then a. (|z|)(m a x)=(1+sqrt(5))/2 b. (|z|)(m in)=(s...

    Text Solution

    |

  2. zo is one of the roots of the equation z^n cos theta0+ z^(n-1) cos th...

    Text Solution

    |

  3. If a0, a1, a2, a3 are all the positive, then 4a0x^3+3a1x^2+2a2x+a3=0 ...

    Text Solution

    |

  4. If 1,z1,z2,z3,.......,z(n-1) be the n, nth roots of unity and omega b...

    Text Solution

    |

  5. If a x ^2+b x+c=0 has imaginary roots and a-b+c >0 then the set of p...

    Text Solution

    |

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

    Text Solution

    |

  7. If the equation z^3 + (3 + i)(z^2) - 3z - (m + i)= 0, m in R , has at ...

    Text Solution

    |

  8. If a+b+c=0,a^2+b^2+c^2=4,t h e na^4+b^4+c^4 is.

    Text Solution

    |

  9. Let P(x) and Q(x) be two polynomials. If f(x) = P(x^4) + xQ(x^4) is di...

    Text Solution

    |

  10. Find the solution set of the system x+2y+z=1 2x-3y-w=2 xgeq0,ygeq0,zge...

    Text Solution

    |

  11. If a m p(z1z2)=0a n d|z1|=|z2|=1,t h e n z1+z2=0 b. z1z2=1 c. z1=z 2...

    Text Solution

    |

  12. mn squares of equal size are arranged to form a rectangle of dimension...

    Text Solution

    |

  13. If the points A(z),B(-z),a n dC(1-z) are the vertices of an equilater...

    Text Solution

    |

  14. Form a quadratic equation whose roots are -4a n d6.

    Text Solution

    |

  15. If |(z-z1)/(z-z2)|=3,w h e r ez1a n dz2 are fixed complex numbers and ...

    Text Solution

    |

  16. If a,b,c are odd integere then about that ax^2+bx+c=0, does not have r...

    Text Solution

    |

  17. if arg(z+a)=pi/6 and arg(z-a)=(2pi)/3 then

    Text Solution

    |

  18. Values (s)(-i)^(1/3) is/are (sqrt(3)-i)/2 b. (sqrt(3)+i)/2 c. (-sqrt(...

    Text Solution

    |

  19. if costheta , sinphi , sintheta are in g.p then check the nature of ro...

    Text Solution

    |

  20. Given z=(1+isqrt(3))^(100), then [Re(z)//Im(z)] equals (a)2^(100) b. 2...

    Text Solution

    |