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How many real solutions does the equatio...

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

A

7

B

1

C

3

D

5

Text Solution

Verified by Experts

The correct Answer is:
B
Let f(x)`=x^(7)+14x^(5)+16x^(3)+30x=560`.
Clearly, f'(x)=0 is an odd degree equation. So, it has at least one real root.
`:' f'(x)=7x^(6)+70x^(4)+48x^(2)+30 gt 0` for all `x in R`
`rArr` f(x) is increasing on R.
So, y=f(x) crosses x-asis exactly once.
Hence, f(x)=0 has exactly one real root.
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OBJECTIVE RD SHARMA ENGLISH-MISCELLANEOUS EQUATIONS AND INEQUATIONS -Chapter Test
  1. How many real solutions does the equation x^(7)=14x^(5)+16x^(3)+30x-56...

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  2. If 3^(x)+2^(2x) ge 5^(x), then the solution set for x, is

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  3. The number of real solutions of the equation 1-x=[cosx] is

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  4. The number of solutions of [sin x+cos x]=3+[-sin x]+[-cos x] in the ...

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  5. Let x=(a+2b)/(a+b) and y=(a)/(b), where a and b are positive integers....

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  6. The solution set contained in Rof the following inequation3^x+3^(1-x)...

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  7. If 0lt x lt pi//2 and sin^(n) x+ cos^(n) x ge 1 , then

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  8. The number of real roots of the equation x^(2)+x+3+2 sin x=0, x in [...

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  9. The number of real roots of the equation 1+3^(x//2)=2^(x), is

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  10. Total number of solutions of the equation sin pi x=|ln(e)|x|| is :

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  11. The number of roots of the equation [sin^(-1)x]=x-[x], is

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  12. The number of values of a for which the system of equations 2^(|x|)+|x...

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  13. The number of real solutions (x, y, z, t) of simultaneous equations 2y...

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  14. If the sum of the greatest integer less than or equal to x and the lea...

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  15. If x,y and z are real such that x+y+z=4, x^(2)+y^(2)+z^(2)=6, x belong...

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  16. Consider the equation : x^(2)+198x+30=2sqrt(x^(2)+18x+45)

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  17. x^(8)-x^(5)-(1)/(x)+(1)/(x^(4)) gt 0, is satisfied for

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  18. The number of solutions of the equation ((1+e^(x^(2)))sqrt(1+x^(2)))...

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  19. The number of real roots of the equation 1+a(1)x+a(2)x^(2)+………..a(n)...

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  20. Let a,b be integers and f(x) be a polynomial with integer coefficients...

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  21. Let Pn(ix) =1+2x+3x^2+............+(n+1)x^n be a polynomial such that...

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