Home
Class 11
MATHS
If p ,q are real p!=q , then show that t...

If `p ,q` are real `p!=q ,` then show that the roots of the equation `(p-q)x^2+5(p+q)x-2(p-q)=0` are real and unequal.

A

real and equal

B

unequal and rational

C

unequal and irrational

D

nothing can be said

Text Solution

Verified by Experts

The correct Answer is:
D
The discriminant D of the given equation is `D = 25 (p+q)^(2) + 8(p-q)^(2)+4r(p-q)`
Clearly, its sign cannot be determined.
So, nothing can be said about the nature of roots.
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|123 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|22 Videos

  • PROBABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|45 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|59 Videos

Similar Questions

Explore conceptually related problems

If p , qr are real and p!=q , then show that the roots of the equation (p-q)x^2+5(p+q)x-2(p-q=0 are real and unequal.

If the roots of the equation qx^(2)+2px+2q=0 are real and unequal, prove that the roots of the equation (p+q)x^(2)+2qx+(p-q)=0 are imaginary.

If p,q,r,s are real and prgt4(q+s) then show that at least one of the equations x^2+px+q=0 and x^2+rx+s=0 has real roots.

If p , q , ra n ds are real numbers such that p r=2(q+s), then show that at least one of the equations x^2+p x+q=0 and x^2+r x+s=0 has real roots.

If the roots of the equation (1-q+p^(2)/2)x^(2) + p(1+q)x+q(q-1) +p^(2)/2=0 are equal, then show that p^(2) = 4q

If p ,q ,r are positive and are in A.P., the roots of quadratic equation p x^2+q x+r=0 are all real for a. |r/p-7|geq4sqrt(3) b. |p/r-7|geq4sqrt(3) c. all p and r d. no p and r

If 2+sqrt(3)i is a root of the equation x^2+p x+q=0 , then write the values of p\ a n d\ q .

Show that if p,q,r and s are real numbers and pr=2(q+s) , then atleast one of the equations x^(2)+px+q=0 and x^(2)+rx+s=0 has real roots.

If a ,b ,p ,q are non zero real numbers, then how many comman roots would two equations: 2a^2x^2-2a b x+b^2=0 and p^2x^2+2p q x+q^2=0 have?

Show that the sequence (p + q)^(2), (p^(2) + q^(2)), (p-q)^(2) … is an A.P.

OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Chapter Test
  1. If p ,q are real p!=q , then show that the roots of the equation (p-q)...

    Text Solution

    |

  2. The set of values of a for which x^2+ax+sin^(-1)(x^2-4x+5)+cos^(-1)(x^...

    Text Solution

    |

  3. The set of possible values of lambda for which x^2-(lambda^2-5 lambda...

    Text Solution

    |

  4. The equation (a + 2)x^2 + (a-3)x = 2a - 1, a != -2 has roots rational ...

    Text Solution

    |

  5. If cos alpha, sin beta, sin alpha are in increasing G.P. , then roots ...

    Text Solution

    |

  6. If alpha,beta are roots of x^2-3x+a=0,a in Ra n dalpha<1<beta, then f...

    Text Solution

    |

  7. If the equations ax^2+bx+c=0 and cx^2+bx+a=0, a!=c have a negative com...

    Text Solution

    |

  8. If the roots of the equation x^3-12x^2 +39x -28 =0 are in AP, then the...

    Text Solution

    |

  9. If the roots of a1x^2 + b1x+ c1 = 0 are alpha1 ,beta 1 and those o...

    Text Solution

    |

  10. If the roots of the equation ax^(2)-4x+a^(2)=0 are imaginery and the s...

    Text Solution

    |

  11. If a, b, c are positive real numbers, then the roots of the equation a...

    Text Solution

    |

  12. If the absolute value of the difference of the roots of the equation x...

    Text Solution

    |

  13. If alpha, beta be roots of the equation 375x ^(2) -25x-2=0 and s (n) =...

    Text Solution

    |

  14. The quadratic equation x^(2) + (a^(2) - 2) x - 2a^(2) and x^(2) - 3x +...

    Text Solution

    |

  15. The roots of ax^(2) +bx +c =0 " whose " a ne 0, b ,c in R , " are non...

    Text Solution

    |

  16. The value of m for which the equation x^3-mx^2+3x-2=0 has two roots ...

    Text Solution

    |

  17. If the equation formed by decreasing each root of the a x^2+b x+c=0 by...

    Text Solution

    |

  18. If the roots of the equation ax^2-bx-c=0 are changed by same quantity ...

    Text Solution

    |

  19. If x^2-2rprx+r=0; r=1, 2,3 are three quadratic equations of which each...

    Text Solution

    |

  20. If x ^(2) + px +1 is a factor of ax ^(3) + bx +c, then:

    Text Solution

    |

  21. If (x-1)^3 is a factor of x^4+ax^3+bx^2+cx-1=0 then the other factor ...

    Text Solution

    |