Home
Class 12
MATHS
If the equations 2x^(2)-7x+1=0 and ax^(2...

If the equations `2x^(2)-7x+1=0` and `ax^(2)+bx+2=0` have a common root, then

A

`a=2`, `b=-7`

B

`a=(-7)/(2)`, `b=1`

C

`a=4`, `b=-14`

D

`a=-4`, `b=1`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` First equation has irrational roots.
Therefore, both roots are common
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|6 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise ILLUSTRATION|121 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

If the equation x^2+ax+bc=0" and " x^2+bx+ca=0 have a common root, then a+b+c =

If the equations x^2 + 2x + 3 = 0 and ax^2 + bx + + c = 0 have common root, then a : b : c is _____

If the equation x^2-cx+d=0 and x^2-ax+b=0 have a common root,and the roots of the second equations are equal ,then prove that 2(b+d)=ac

Find those values of k for which the equations x^2-kx-21=0 and x^2-3kx-35=0 have a common root.

If the equations x^2+ax+b=0 and x^2+bx+a=0 have one common root. Then find the numerical value of a+b.

If the quadratic equations ax^2+2cx+b =0 and ax^2+2bx+c =0 (b ne 0) have a common root, then a+4b+4c is equal to

If the two equations x^2+ax+b=0 and x^2+bx+a=0 ( aneb ) have a common root, show that the other roots are the roots of the equation x^2+x+ab=0 .

The equations x^(2)+x+a=0andx^(2)+ax+1=0 have a common root-

If a, b, c are in G.P. and the equation ax^(2) + 2bx + c = 0 and dx^(2) + 2ex + f = 0 have a common root, then show that (d)/(a), (e)/(b), (f)/(c ) are in A.P.

CENGAGE PUBLICATION-THEORY OF EQUATIONS-Single correct Answer
  1. If alpha and beta be the roots of equation x^(2) + 3x + 1 = 0 then the...

    Text Solution

    |

  2. The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are, when ab...

    Text Solution

    |

  3. If the equations 2x^(2)-7x+1=0 and ax^(2)+bx+2=0 have a common root, t...

    Text Solution

    |

  4. If alphaa n dbeta,alphaa n dgamma,alphaa n ddelta are the roots of the...

    Text Solution

    |

  5. The product of uncommon real roots of the polynomials p(x)=x^4+2x^3-8...

    Text Solution

    |

  6. Number of values of x satisfying the pair of quadratic equations x^(2)...

    Text Solution

    |

  7. If the equation 4x^2-x-1=0 and 3x^2+(lambda+mu)x+lambda-mu=0 have a r...

    Text Solution

    |

  8. If the equations x^(2)+2lambdax+lambda^(2)+1=0, lambda in R and ax^(2)...

    Text Solution

    |

  9. If both the roots of lamda(6x^(2)+3)+rx+2x^(2)-1=0 and 6 lamda(2x^(2)+...

    Text Solution

    |

  10. x^(3)+5x^(2)+px+q=0 and x^(3)+7x^(2)+px+r=0 have two roos in common. I...

    Text Solution

    |

  11. Let a,b in N, a != b and the two quadratic equations (a-1)x^2-(a^2+2)x...

    Text Solution

    |

  12. A quadratic equations p(x)=0 having coefficient x^(2) unity is such th...

    Text Solution

    |

  13. If ax^2+bx+c=0 and cx^2+bx+a=0 (a,b,cinR) have a common non-real roots...

    Text Solution

    |

  14. Consdier the equaiton 2 + |x^(2) + 4x + 2= m , m in R Set of all ...

    Text Solution

    |

  15. If the equation |x^2-5x + 6|-lambda x+7 lambda=0 has exactly 3 distin...

    Text Solution

    |

  16. Let alpha, beta (a lt b) be the roots of the equation ax^(2)+bx+c=0. I...

    Text Solution

    |

  17. If the quadratic polynomials defined on real coefficient P(x)=a(1)x^...

    Text Solution

    |

  18. For which of the following graphs the quadratic expression y=ax^(2)+bx...

    Text Solution

    |

  19. The difference of maximum and minimum value of (x^(2)+4x+9)/(x^(2)+9) ...

    Text Solution

    |

  20. If a gt 1 , then the roots of the equation (1-a)x^(2)+3ax-1=0 are

    Text Solution

    |