Home
Class 12
MATHS
If a(p+q)^2+2b p q+c=0 and a(p+r)^2+2b p...

If `a(p+q)^2+2b p q+c=0 and a(p+r)^2+2b p r+c=0 (a!=0)` , then which one is correct? a) `q r=p^2` b) `q r=p^2+c/a` c) none of these d) either a) or b)

A

`qr=p^(2)+(c)/(a)`

B

`qr=p^(2)`

C

`qr=-p^(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise Numerical value type of JEE Main|15 Videos

  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Main ( Archive )|20 Videos

  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advance ( Archive )|20 Videos

  • PROPERTIES OF TRIANGLE

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|50 Videos

  • QUIZ

    VMC MODULES ENGLISH|Exercise MATHEMATICS|30 Videos

Similar Questions

Explore conceptually related problems

If p/a + q/b + r/c=1 and a/p + b/q + c/r=0 , then the value of p^(2)/a^(2) + q^(2)/b^(2) + r^(2)/c^(2) is:

p+r+2q= 1 b. 2 c. 0 d. 4

If A B C~= P Q R and A B C is not congruent to R P Q , then which of the following not true: (a) B C=P Q (b) A C=P R (c) A B=P Q (d) Q R=B C

If the normals to the parabola y^2=4a x at three points (a p^2,2a p) and (a q^2,2a q) and (a r^2,2ar) are concurrent, then the common root of equations P x^2+q x+r=0 and a(b-c)x^2+b(c-a)x+c(a-b)=0 is (a) p (b) q (c) r (d) 1

If a!=p ,b!=q ,c!=r and |[p, b, c ],[a, q, c ],[a ,b, r]|=0, then find the value of p/(p-a)+q/(q-b)+r/(r-c)dot

|(a+1, a+2, a+p), (a+2, a+3, a+q) ,(a+3, a+4, a+r)|=0 , then p, q r are in (A) A P (B) G P (C) H P (D) none of these

If a , b and c b respectively the pth , qth and rth terms of an A.P. prove that a(q-r) +b(r-p) +c (p-q) =0

If the normals to the parabola y^2=4a x at three points (a p^2,2a p), and (a q^2,2a q) are concurrent, then the common root of equations P x^2+q x+r=0 and a(b-c)x^2+b(c-a)x+c(a-b)=0 is p (b) q (c) r (d) 1

If a,b,c, be the pth, qth and rth terms respectivley of a G.P., then the equation a^q b^r c^p x^2 +pqrx+a^r b^-p c^q=0 has (A) both roots zero (B) at least one root zero (C) no root zero (D) both roots unilty

If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],[ q c ,r a, p b],[ r b, p c, q a]|i s (a) 0 (b) p a+q b+r c (c) 1 (d) none of these

VMC MODULES ENGLISH-QUADRATIC EQUATIONS & INEQUATIONS -LEVEL -2
  1. The polynomiaal (a x^2+b x+c)(a x^2-dx-c), a c!=0 has

    Text Solution

    |

  2. If the equation ax^(2)+2bx-3c=0 has no real roots and ((3c)/(4))lta+b,...

    Text Solution

    |

  3. If a(p+q)^2+2b p q+c=0 and a(p+r)^2+2b p r+c=0 (a!=0) , then which one...

    Text Solution

    |

  4. If alpha and beta(alpha lt beta) are the roots of the equation x^(2)+b...

    Text Solution

    |

  5. The number of real solutions of the equation (9//10)^x=-3+x-x^2 is

    Text Solution

    |

  6. If the roots of a1x^(2)+b1x+c1=0 and alpha1 , beta1 and those of a2...

    Text Solution

    |

  7. If b^2>4ac, then a(x^2 +4x+4)^2+b(x^2 +4x +4)+c=0 has distinct real ...

    Text Solution

    |

  8. If ( lambda^(2) + lambda - 2)x^(2)+(lambda+2)x lt 1 for all x in R ,...

    Text Solution

    |

  9. The value of k for which the equation (k-2) x^(2) + 8x + k + 4 = 0 has...

    Text Solution

    |

  10. For all x in R if mx^(2) - 9mx + 5m + 1 gt 0 , then m lies in the in...

    Text Solution

    |

  11. The quadratic equations x^2""-6x""+""a""=""0""a n d ""x^2""-c x""+""...

    Text Solution

    |

  12. If roots of ax^2+bx+c=0 are equal in magnitude but opposite in sign, t...

    Text Solution

    |

  13. If alpha ne beta but alpha^(2)= 5 alpha - 3 and beta ^(2)= 5 beta...

    Text Solution

    |

  14. lf 0 < a < b < c < d, then the quadratic equation ax^2 + ...

    Text Solution

    |

  15. If alpha,beta are the roots of the equation ax^2 + bx +c=0 such that b...

    Text Solution

    |

  16. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, t...

    Text Solution

    |

  17. Consider the equation |x^2-2x- 3|=m .m belongs to R .If the given equa...

    Text Solution

    |

  18. Consider the equation |x^2-2x- 3|=m .m belongs to R .If the given equa...

    Text Solution

    |

  19. Consider the equation |x^(2)-2x-3|=m , m in R . If the given equatio...

    Text Solution

    |

  20. Let f (x) =ax ^(2) +bx + c,a ne 0, such the f (-1-x)=f (-1+ x) AA x in...

    Text Solution

    |