Home
Class 12
MATHS
How many real solutions does the equatio...

How many real solutions does the equation `x^7+14 x^5+16 x^3+30 x-560=0` have?

A

1

B

3

C

5

D

7

Text Solution

Verified by Experts

The correct Answer is:
A
Let `f(x)=x^(7)+14x^(5)+16x^(3)+30x-560`
`:'f'(x)=7x^(6)+70x^(4)+48x^(2)+30gt0, AA x epsilonR`
`impliesf(x)` is an increasing function, for all `x epsilonR`
Hence number of real solution is 1.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|24 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|44 Videos

Similar Questions

Explore conceptually related problems

How many real solution does the equation x^(7)+14x^(5)+16x^(3)+30x-560=0 have?

How many real solutions does the equation x^(7)+14x^(5)+16x^(3)+30x-560=0 have?

How many real solutions does the equation x^(7)+14x^(5)+16x^(3)+30x-560=0 have? (1)7(2)1(3)3(4)5

Find the solutions of the equation : 3x^2 - 7x - 6 = 0

Maximum number of real solution does the equation x^(7)+ax^(5)+bx^(3)+cx-d=0 can have?

How many real roots does the quadratic equation f(x) = x^(2) + 3 |x|+2 = 0 have ?

ARIHANT MATHS-THEORY OF EQUATIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let a, b, c, p, q be the real numbers. Suppose alpha,beta are the ...

    Text Solution

    |

  2. The quadratic equations x^2""6x""+""a""=""0""a n d""x^2""c x""+""6"...

    Text Solution

    |

  3. How many real solutions does the equation x^7+14 x^5+16 x^3+30 x-560=0...

    Text Solution

    |

  4. Suppose the cubic x^(3)-px+q has three distinct real roots, where pgt0...

    Text Solution

    |

  5. The smallest value of k, for which both the roots of the equation, x^2...

    Text Solution

    |

  6. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, ...

    Text Solution

    |

  7. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

    Text Solution

    |

  8. Conder the function f(x)=1+2x+3x^2+4x^3 Let the sum of all distinct ...

    Text Solution

    |

  9. Let alpha and beta be the roots of x^2-6x-2=0 with alpha>beta if an=al...

    Text Solution

    |

  10. The value of b for which the equation x^2+bx-1=0 and x^2+x+b=0 have on...

    Text Solution

    |

  11. The number of distinct real roots of x^4 - 4 x^3 + 12 x^2 + x - 1 = 0...

    Text Solution

    |

  12. Let for a != a1 != 0 , f(x)=ax^2+bx+c ,g(x)=a1x^2+b1x+c1 and p(x) = f(...

    Text Solution

    |

  13. 8. Sachin and Rahul attempted to solve a quadratic equation. Sachin ma...

    Text Solution

    |

  14. let alpha(a) and beta(a) be the roots of the equation ((1+a)^(1/3)-1)x...

    Text Solution

    |

  15. Show that the equation e^(sinx)-e^(-sinx)-4=0 has no real solution.

    Text Solution

    |

  16. If the equation x^2+2x+3=0 and ax^2+bx+c=0 have a common root then a:...

    Text Solution

    |

  17. If a in R and the equation -3(x-[x])^2+""2""(x-[x])""+a^2=""0 (whe...

    Text Solution

    |

  18. Let alpha and beta be the roots of equation px^2 + qx + r = 0 , p != ...

    Text Solution

    |

  19. Let a in R and let f: R to R be given by f(x) =x^(5) -5x+a. then

    Text Solution

    |

  20. The quadratic equation p(x)=0 with real coefficients has purely imagin...

    Text Solution

    |