Home
Class 11
MATHS
If x^3+3x^2-9x+c is of the form (x-alph...

If `x^3+3x^2-9x+c` is of the form `(x-alpha)^2(x-beta)` , then `c` is equal to a.`27` b. `-27` c. `5` d. `-5`

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 x^(3)+3x^(2)-9x+lamda is of the form (x-alpha)^(2)(x-beta) then lamda is equal to

If x ,2x+2 and 3x+3 are the first three terms of a G.P., then the fourth term is a. 27 b. -27 c. 13.5 d. -13.5

If alpha,beta,gamma,sigma are the roots of the equation x^4+4x^3-6x^2+7x-9=0, then the value of (1+alpha^2)(1-beta^2)(1-gamma^2)(1-sigma^2) is a. -75 b. 25 c. 0 d. 75

If tanalpha is equal to the integral solution of the inequality 4x^2-16 x+15<0 and cosbeta is equal to the slope of the bisector of the first quadrant, then sin(alpha+beta)sin(alpha-beta) is equal to (a) 3/5 (b) 3/5 (c) 2/(sqrt(5)) (d) 4/5

Let alpha,beta be the roots of the equation (x-a)(x-b)=c ,c!=0. Then the roots of the equation (x-alpha)(x-beta)+c=0 are a , c b. b , c c. a , b d. a+c , b+c

Let |(x,2,x),(x^2,x,6),(x,x,6)|=A x^4+B x^3+C x^2+D x+Edot Then the value of 5A+4B+3C+2D+E is equal to a. zero b. -16 c. 11 d. -11

If alpha and beta be the roots of equation x^(2) + 3x + 1 = 0 then the value of ((alpha)/(1 + beta))^(2) + ((beta)/(1 + alpha))^(2) is equal to

If alpha and beta be the roots of the equation 5x^2+bx+c=0 Show that 5x^2+bx+c=5(x-alpha)(x-beta) Show also that for all real values of x the expression 5x^2+bx+c cannot be negative if alpha and beta are real and equal

If f(x) = 27x^3 + 1/x^3 and alpha, beta are the roots of 3x + 1/x = 2 then

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If a r g["z"1("z"3-"z"2)]=a r g["z"3("z"2-"z"1)] , then prove that O ,...

    Text Solution

    |

  2. If x" - "i y" "=sqrt((a-i b)/(c-i d)) prove that (x^2+y^2)^2=(a^2+b^2...

    Text Solution

    |

  3. If x^3+3x^2-9x+c is of the form (x-alpha)^2(x-beta) , then c is equ...

    Text Solution

    |

  4. If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...

    Text Solution

    |

  5. If z=(a+ib)^5+(b+ia)^5 then prove that Re(z)=Im(z), where a,b in R.

    Text Solution

    |

  6. If a and b are positive numbers and eah of the equations x^2+a x+2b=0 ...

    Text Solution

    |

  7. Find the real values of x and y for which the following equation is sa...

    Text Solution

    |

  8. The three angular points of a triangle are given by Z=alpha, Z=beta,Z=...

    Text Solution

    |

  9. Suppose a ,b ,c are the roots of the cubic x^3-x^2-2=0. Then the value...

    Text Solution

    |

  10. It is given that n is an odd integer greater than 3 but n is not a mul...

    Text Solution

    |

  11. If alpha,beta,gamma,delta are four complex numbers such that gamma/del...

    Text Solution

    |

  12. If ax^(2)+(b-c)x+a-b-c=0 has unequal real roots for all c epsilon R, ...

    Text Solution

    |

  13. If z1^2+z2^2+2z1.z2.costheta= 0 prove that the points represented by ...

    Text Solution

    |

  14. Prove that the circles z bar z +z( bar a 1)+bar z( a1 )+b1=0 ,b1 in ...

    Text Solution

    |

  15. If a , b ,c real in G.P., then the roots of the equation a x^2+b x+c=0...

    Text Solution

    |

  16. If z0 is the circumcenter of an equilateral triangle with vertices z1,...

    Text Solution

    |

  17. Two different non-parallel lines cut the circle |z| = r at points a...

    Text Solution

    |

  18. If the equations x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0 have a com...

    Text Solution

    |

  19. Prove that |z-z1|^2+|z-z2|^2=k will represent a real circle with cente...

    Text Solution

    |

  20. Complex numbers z1 , z2 , z3 are the vertices A, B, C respectively of ...

    Text Solution

    |