Home
Class 11
MATHS
If a lt b lt c lt d, then for any real ...

If `a lt b lt c lt d`, then for any real non-zero `lambda`, the quadratic equation `(x-a)(x-c)+lambda(x-b)(x-d)=0`,has (a) no real roots. (b) one real root between a and c (c) one real root between b and d (d) Irrational roots.

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos
  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If altbltcltd , then the roots of equation (x-a)(x-c)+2(x-b)(x-d)=0 , are

Prove that the quadratic equation (a^2+b^2)x^2+2(ac+bd)x+(c^2+d^2)=0 has no real roots when ad!=bc .

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a) 6 real roots b) at least 2 real roots c) 4 real roots d) none of these

Prove that both the roots of the equation (x-a)(x-b)+ (x-b)(x-c)+(x-a)(x-c)=0 are real.

The equation (log)_(x+1)(x- .5)=(log)_(x-0. 5)(x+1) has (A) two real solutions (B) no prime solution (C) one integral solution (D) no irrational solution

The equation x-2/(x-1)=1-2/(x-1) has a. no root b. one root c. two equals roots d. Infinitely many roots

If a ,b ,c ,d are four consecutive terms of an increasing A.P., then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are a. non-real complex b. real and equal c. integers d. real and distinct

Find the values of p for which the equation x^(4)-14x^(2)+24x-3-p=0 has (a) Two distinct negative real roots (b) Two real roots of opposite sign (c) Four distinct real roots (d) No real roots

If the roots of the quadratic equation (b-c)x^(2)+(c-a)x+(a-b)=0 are real and equal then prove that 2b=a+c.

If a, b, c are real, then both the roots of the equation (x -b )(x -c)+(x -c)(x - a)+(x - a)(x - b)=0 are always

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If alpha,beta are roots of x^2-3x+a=0 , a in R and alpha &lt;1< beta...

    Text Solution

    |

  2. If z=x+iy and x^(2)+y^(2)=16, then the range of abs(abs(x)-abs(y)) is

    Text Solution

    |

  3. If a lt b lt c lt d, then for any real non-zero lambda, the quadratic...

    Text Solution

    |

  4. If k>0, |z|=|w|=k, and alpha=(z-bar w)/(k^2+zbar(w)), then Re(alpha) ...

    Text Solution

    |

  5. The quadratic x^2+a x+b+1=0 has roots which are positive integers, th...

    Text Solution

    |

  6. if z1 and z2 are two complex numbers such that absz1lt1ltabsz2 then p...

    Text Solution

    |

  7. The sum of values of x satisfying the equation (31+8sqrt(15))^(x^2-3)+...

    Text Solution

    |

  8. Let a complex number alpha,alpha!=1, be a root of the equation z^(p+q)...

    Text Solution

    |

  9. If alpha,beta are real and distinct roots of a x^2+b x-c=0 and p ,q ar...

    Text Solution

    |

  10. Let a!=0 and p(x) be a polynomial of degree greater than 2. If p(x) le...

    Text Solution

    |

  11. Prove that there exists no complex number z such that |z| &lt; 1/3 an...

    Text Solution

    |

  12. A quadratic equation with integral coefficients has two different prim...

    Text Solution

    |

  13. find the centre and radius of the circle formed by all the points repr...

    Text Solution

    |

  14. If a ,b ,c are three distinct positive real numbers, the number of rea...

    Text Solution

    |

  15. Find the non-zero complex number z satisfying z =i z^2dot

    Text Solution

    |

  16. Let a,b and c be real numbers such that 4a+2b+c=0 and ab gt 0.Then t...

    Text Solution

    |

  17. If |z|<=1,|w|<=1, then show that |z- w|^2<=(|z|-|w|)^2+(argz-argw)^2

    Text Solution

    |

  18. If alpha,beta are the roots of the equation x^2-2x+3=0 obtain the equa...

    Text Solution

    |

  19. For complex numbers z and w prove that absz^2w-abs(w)^2z=z-w if and on...

    Text Solution

    |

  20. If alpha,beta are the roots of the equation a x^2+b x+c=0, then the va...

    Text Solution

    |