Home
Class 11
MATHS
If alpha1,alpha2 are the roots of equat...

If `alpha_1,alpha_2` are the roots of equation `x ^2-p x+1=0a n dbeta_1,beta_2` are those of equation `x^2-q x+1=0` and vector `alpha_1 hat i+beta_1 hat j` is parallel to `alpha_2 hat i+beta_2 hat j` , then `p=
a. +-q` b. `p=+-2q` c. `p=2q` 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 alpha_1, alpha_2 be the roots of the equation x^2-px+1=0 and beta_1,beta_2 be those of equatiion x^2-qx+1=0 and vecu=alpha_1hati+alpha_2hatj,and vecv=beta_1hati+beta_2hatj is parallel.

If alpha_1, alpha_2 be the roots of equation x^2+px+q=0 and beta_1,beta be those of equation x^2+rx+s=0 and the system of equations alpha_1y+alpha_2z=0 and beta_1 y+beta_2 z=0 has non trivial solution, show that p^2/r^2=q/s

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0. a n dalpha^2,beta are the roots of quadratic equation x^2-q x+8=0, then find p ,q,alpha,betadot

If alpha , beta are the roots of x^2-p(x+1)+c=0 then (1+alpha )( 1+ beta )=

If alpha, beta are the roots of the equations x^2+px+q=0 then one of the roots of the equation qx^2-(p^2-2q)x+q=0 is (A) 0 (B) 1 (C) alpha/beta (D) alpha beta

If alpha and beta are the roots of the equation x^2+4x + 1=0(alpha > beta) then find the value of 1/(alpha)^2 + 1/(beta)^2

If alphabeta the roots of the equation x^2-x-1=0 , then the quadratic equation whose roots are (1 + alpha)/(2 -alpha),(1 + beta)/(2 - beta)

If alpha,beta are the roots of the equation x^2+p x+q=0,t h e n-1/alpha,-1/beta are the roots of the equation (a) x^2-p x+q=0 (b) x^2+p x+q=0 (c) q x^2+p x+1=0 (d) q x^2-p x+1=0

If alpha,beta,gamma are the roots of the equation x^3-p x+q=0, then find the cubic equation whose roots are alpha/(1+alpha),beta/(1+beta),gamma/(1+gamma) .

If alpha , beta are the roots of the equation x^(2)-px+q=0 , then (alpha^(2))/(beta^(2))+(beta^(2))/(alpha^(2)) is equal to :

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If alphabeta the roots of the equation x^2-x-1=0 , then the quadratic...

    Text Solution

    |

  2. 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

    |

  3. If alpha1,alpha2 are the roots of equation x ^2-p x+1=0a n dbeta1,bet...

    Text Solution

    |

  4. Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2 , B=b^2c+b c^2-...

    Text Solution

    |

  5. The integral value of m for which the root of the equation m x^2+(2m-1...

    Text Solution

    |

  6. If b1. b2=2(c1+c2) then at least one of the equation x^2+b1x+c1=0 and ...

    Text Solution

    |

  7. If the root of the equation (a-1)(x^2-x+1)^2=(a+1)(x^4+x^2+1) are rea...

    Text Solution

    |

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

    Text Solution

    |

  9. If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx...

    Text Solution

    |

  10. Graph of y = f(x) is as shown in the following figure. Find th...

    Text Solution

    |

  11. In how many points graph of y=x^3-3x^2+5x-3 intersect the x-axis?

    Text Solution

    |

  12. The quadratic polynomial p(x) has the following properties:p(x)geq0 fo...

    Text Solution

    |

  13. If (1-p) is a root of quadratic equation x^2+p x+(1-p)=0, then find it...

    Text Solution

    |

  14. A polynomial in x of degree 3 vanishes when x=1 and x=-2 , ad has the ...

    Text Solution

    |

  15. Let f(x)=a^2+b x+c where a ,b , c in R and a!=0. It is known that f(5...

    Text Solution

    |

  16. If x=1 and x=2 are solutions of equations x^3+a x^2+b x+c=0 and a+b=1,...

    Text Solution

    |

  17. If x in R ,a n da ,b ,c are in ascending or descending order of magni...

    Text Solution

    |

  18. Prove that graphs y=2x-3 and y=x^2-x never intersect.

    Text Solution

    |

  19. Which of the following pair of graphs intersect? y=x^2-xa and y=1 y...

    Text Solution

    |

  20. If alphaa n dbeta are the rootsof he equations x^2-a x+b=0a n dAn=alp...

    Text Solution

    |