Home
Class 11
MATHS
If sec alpha and alpha are the roots of...

If sec `alpha and alpha` are the roots of `x^2-p x+q=0,` then (a) `p^2=q(q-2)` (b) `p^2=q(q+2)` (c)`p^2q^2=2q` (d) none of these

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the quadratic equation given the roots \( \sec \alpha \) and \( \alpha \). The equation is: \[ x^2 - px + q = 0 \] ### Step 1: Use the properties of roots From Vieta's formulas, we know that: ...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

If secalpha and cosecalpha are the roots of the equation x^2-px+q=0 , then (i) p^2=q(q-2) (ii) p^2=q(q+2) (iii) p^2+q^2=2q (iv) none of these

If p and q are the roots of x^2 + px + q = 0 , then find p.

If p and q are the roots of the equation x^2-p x+q=0 , then (a) p=1,\ q=-2 (b) p=1,\ q=0 (c) p=-2,\ q=0 (d) p=-2,\ q=1

If the difference of the roots of x^2-p x+q=0 is unity, then a) p^2+4q=1 b) p^2-4q=1 c) p^2+4q^2=(1+2q)^2 d) 4p^2+q^2=(1+2p)^2

If p != 0, q != 0 and the roots of x^(2) + px +q = 0 are p and q, then (p, q) =

If zeros of the polynomial f(x)=x^3-3p x^2+q x-r are in A.P., then (a) 2p^3=p q-r (b) 2p^3=p q+r (c) p^3=p q-r (d) None of these

If alpha,beta are the roots of a x^2+b x+c=0a n dalpha+h ,beta+h are the roots of p x^2+q x+r=0t h e nh= -1/2(a/b-p/q) b. (b/a-q/p) c. 1/2(b/q-q/p) d. none of these

The value of p and q(p!=0,q!=0) for which p ,q are the roots of the equation x^2+p x+q=0 are (a) p=1,q=-2 (b) p=-1,q=-2 (c) p=-1,q=2 (d) p=1,q=2

If the ratio of the roots of a x ^2+2b x+c=0 is same as the ratios of roots of p x^2+2q x+r=0, then a. (2b)/(a c)=(q^2)/(p r) b. b/(a c)=(q^)/(p r) c. (b^2)/(a c)=(q^2)/(p r) d. none of these

If alpha,beta are the roots of the equation x^2+p x+1=0;gamma,delta the roots of the equation x^2+q x+1=0 , then (alpha-gamma)(alpha+delta)(beta-gamma)(beta+delta)= (a) q^2-p^2 (b) p^2-q^2 (c) p^2=q^2 (d) none of these

CENGAGE ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. In triangle A B C ,ifPdotQ ,R divides sidesB C ,A C , and A B , respec...

    Text Solution

    |

  2. Find the general value of theta which satisfy both sintheta=-1/2a n d...

    Text Solution

    |

  3. If sec alpha and alpha are the roots of x^2-p x+q=0, then (a) p^2=...

    Text Solution

    |

  4. Solve the equation sinx+cosx=1

    Text Solution

    |

  5. In the given figure A B is the diameter of the circle, centred at Odot...

    Text Solution

    |

  6. The value of expression (2sin^2 91^@-1)(2sin^2 92^@-1)....(2sin^2 180...

    Text Solution

    |

  7. Solve (tan3x-tan2x)/(1+tan3xtan2x )=1

    Text Solution

    |

  8. In a A B C ,ifA B=x , B C=x+1,/C=pi/3 , then the least integer value ...

    Text Solution

    |

  9. Solve tanx+tan2x+tan3x=tanxtan2xtan3x ,x in [0,pi]

    Text Solution

    |

  10. The value of cos(pi/7)+cos((2pi)/7)+cos((3pi)/7)+cos((4pi)/7)+cos((5pi...

    Text Solution

    |

  11. In a triangle A B C ,Da n dE are points on B Ca n dA C , respectivley,...

    Text Solution

    |

  12. A0, A1 ,A2, A3, A4, A5 be a regular hexagon inscribed in a circle of u...

    Text Solution

    |

  13. General solution of tantheta+tan4theta+tan7theta=tanthetatan4thetatan7...

    Text Solution

    |

  14. In triangleABC ,Delta=6, abc=60, r=1 Then the value of 1/a+a/b+a/c is ...

    Text Solution

    |

  15. The total number of solution of the equation sin^4 x +cos^4 x = sin x ...

    Text Solution

    |

  16. The numerical value of tan(pi/3)+2tan((2pi)/3)+4tan((4pi)/3)+8tan((8pi...

    Text Solution

    |

  17. Let the area of triangle ABC be (sqrt3 -1)//2, b = 2 and c = (sqrt3 -1...

    Text Solution

    |

  18. A right triangle has perimeter of length 7 and hypotenuse of length 3....

    Text Solution

    |

  19. General solution of sin^2x-5sinxcosx-6cos^2x=0 is x=npi-pi/4,n in Z...

    Text Solution

    |

  20. In triangle A B C , base B C and area of triangle are fixed. The loc...

    Text Solution

    |