Home
Class 11
MATHS
If a ,b ,c in R^+a n d2b=a+c , then che...

If `a ,b ,c in R^+a n d2b=a+c ,` then check the nature of roots of equation `a x^2+2b x+c=0.`

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 a lt c lt b, then check the nature of roots of the equation (a -b)^(2) x^(2) + 2(a+ b - 2c)x + 1 = 0

if a lt c lt b, then check the nature of roots of the equation (a -b)^(2) x^(2) + 2(a+ b - 2c)x + 1 = 0

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0 where a ,b ,c in Rdot

If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0 are

If alphaa n dbeta,alphaa n dgamma,alphaa n ddelta are the roots of the equations a x^2+2b x+c=0,2b x^2+c x+a=0a d nc x^2+a x+2b=0, respectively, where a, b, and c are positive real numbers, then alpha+alpha^2= a. a b c b. a+2b+c c. -1 d. 0

If alpha is a real root of the quadratic equation a x^2+b x+c=0a n dbeta ils a real root of - a x^2+b x+c=0, then show that there is a root gamma of equation (a//2)x^2+b x+c=0 whilch lies between aa n dbetadot

If a ,b ,c in R such that a+b+c=0a n da!=c , then prove that the roots of (b+c-a)x^2+(c+a-b)x+(a+b-c)=0 are real and distinct.

If a ,b ,c in R such that a+b+c=0a n da!=c , then prove that the roots of (b+c-a)x^2+(c+a-b)x+(a+b-c)=0 are real and distinct.

If a,b,c are in A.P. then the roots of the equation (a+b-c)x^2 + (b-a) x-a=0 are :

If a, b, c are real and a!=b , then the roots ofthe equation, 2(a-b)x^2-11(a + b + c) x-3(a-b) = 0 are :

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If ((1+i)/(1-i))^m=1, then find the least positive integral value of m...

    Text Solution

    |

  2. If ,Z1,Z2,Z3,........Z(n-1) are n^(th) roots of unity then the value ...

    Text Solution

    |

  3. If a ,b ,c in R^+a n d2b=a+c , then check the nature of roots of equa...

    Text Solution

    |

  4. If z is a complex number such taht z^2=( barz)^2, then find the loc...

    Text Solution

    |

  5. If z^3+(3+2i)z+(-1+i a)=0 has one real roots, then the value of a lies...

    Text Solution

    |

  6. Determine the value of k for which x+2 is a factor of (x+1)^7+(2x+k)^3...

    Text Solution

    |

  7. Find the complex number z satisfying R e(z^2 =0),|z|=sqrt(3.)

    Text Solution

    |

  8. Given that the expression 2x^3+3p x^2-4x+p hs a remainder of 5 when di...

    Text Solution

    |

  9. z1a n dz2 are two distinct points in an Argand plane. If a|z1|=b|z2|(w...

    Text Solution

    |

  10. Consider two complex numbers alphaa n dbeta as alpha=[(a+b i)//(a-b i...

    Text Solution

    |

  11. In how many points the graph of f(x)=x^3+2x^2+3x+4 meets the x-axis ...

    Text Solution

    |

  12. If x^2+x+1=0 then the value of (x+1/x)^2+(x^2+1/(x^2))^2+...+(x^27+1/(...

    Text Solution

    |

  13. If (a" "+" "i b)" "(c" "+" "i d)" "(e" "+" "if)" "(g" "+" "i h)" "=" "...

    Text Solution

    |

  14. Analyze the roots of the equation (x-1)^3+(x-2)^3+(x-4)^3+(x-5)^3=0 by...

    Text Solution

    |

  15. Solve the equation |z|=z+1+2idot

    Text Solution

    |

  16. If z=i^(i^(i)) where i=sqrt-1 then |z| is equal to

    Text Solution

    |

  17. Find the values of a for which the roots of the equation x^2+a^2=8x+6...

    Text Solution

    |

  18. If alpha and beta are different complex numbers with |beta|=1, then...

    Text Solution

    |

  19. If z=i log(2-sqrt3), then cosz= a. -1 b. (-1)/2 c. 1 d. 2

    Text Solution

    |

  20. If f(x)=x^3-x^2+a x+b is divisible by x^2-x , then find the value of...

    Text Solution

    |