Home
Class 12
MATHS
If f(x) is a polynomial of degree four ...

If f(x) is a polynomial of degree four with leading coefficient one satisfying `f(1)=1, f(2)=2,f(3)=3`.then `[(f(-1)+f(5))/(f(0)+f(4))]`

A

`4`

B

`5`

C

`6`

D

`7`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` According to question
`f(x)-x=(x-1)(x-2)(x-3)(x-alpha)`
`implies f(-1)=24(1+alpha)-1`
`f(0)=6alpha`
`f(4)=6(4-alpha)+4`
`f(5)=24(5-alpha)+5`
`implies[(f(-1)+f(5))/(f(0)+f(4))]=[(148)/(28)]=5`
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

Let f be twice differentiable function satisfying f(1) = 1, f(2) = 4, f(3) =9 then :

f(x) is a polynomial of degree 4 with real coefficients such that f(x)=0 is satisfied by x=1,2,3 only then f'(1).f'(2).f'(3) is equal to :

If f(x) is a polynomial function satisfying f(x)dotf(1/x)=f(x)+f(1/x) and f(4)=65 ,then find f(6)

Find the polynomial function f(x) of degree 3 for which it is known that f(0) = 1, f(1) = 2, f(2) = 11 and f(3) = 34.

Let f(x) be a polynomial of degree four having extreme values at x=1 and x=2. lim_(xrarr0)[1+f(x)/x^2]=3 ,then f(2) is equal to:

Find the polynomial function f(x) for which it is known that f(0) = 1, f(1) = 2, f(2) = 11 and f(3) = 34.

Find the polynomial function f(x) for which it is known that f(0) = 1, f(1) = 2, f(2) = 11 and f(3) = 34.

2f(x)+3f(-x)=15-4x then [f(1)+f(-1)]=?

If f is a linear function and f(2)=4,f(-1)=3 then find f(x)

Find the degree two polynomial function f(x) for which it is known that f(0) = 1, f(1) = 5, f(2) = 11.

CENGAGE PUBLICATION-THEORY OF EQUATIONS-Single correct Answer
  1. The difference of maximum and minimum value of (x^(2)+4x+9)/(x^(2)+9) ...

    Text Solution

    |

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

    Text Solution

    |

  3. All the values of ' a ' for which the quadratic expression a x^2+(a-2)...

    Text Solution

    |

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

    Text Solution

    |

  5. The equation ax^(4)-2x^(2)-(a-1)=0 will have real and unequal roots if

    Text Solution

    |

  6. If ax^(2)+bx+c=0, a ne 0, a, b, c in R has distinct real roots in (1,2...

    Text Solution

    |

  7. If c lt a lt b lt d, then roots of the equation bx^(2)+(1-b(c+d)x+bcd-...

    Text Solution

    |

  8. If 2a, b, 2c are in A.P. where a, b, c are R^(+), then the expression ...

    Text Solution

    |

  9. If a, b, c are positive numbers such that a gt b gt c and the equation...

    Text Solution

    |

  10. If the quadratic equation x^(2)-36x+lambda=0 has roots alpha and beta ...

    Text Solution

    |

  11. If the equation 2^(2x)+a*2^(x+1)+a+1=0 has roots of opposite sign, the...

    Text Solution

    |

  12. Let a, b, c ne three distinct non-zero real numbers satisfying the sys...

    Text Solution

    |

  13. In the given figure graph of y=p(x)=x^(4)+ax^(3)+bx^(2)+cx+d is given ...

    Text Solution

    |

  14. If a^(3)-3a^(2)+5a-17=0 and b^(3)-3b^(2)+5b+11=0 are such that a+b is ...

    Text Solution

    |

  15. Let f(x) = x^4 + ax^3 + bx^2 + cx + d be a polynomial with real coeffi...

    Text Solution

    |

  16. If f(x) is a polynomial of degree four with leading coefficient one s...

    Text Solution

    |

  17. Let P (x)=x ^(6) -x ^(5) -x ^(3) -x ^(2) -x and alpha, beta, gamma, de...

    Text Solution

    |

  18. The line y=mx+1 touches the curves y=-x^(4)+2x^(2)+x at two points P(x...

    Text Solution

    |

  19. If a+2b+3c=4, then find the least value of a^2+b^2+c^2dot

    Text Solution

    |

  20. If the roots of x^(4)+qx^(2)+kx+225=0 are in arthmetic progression, th...

    Text Solution

    |