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Prove that if 2a0^2lt15a all roots of x^...

Prove that if `2a_0^2lt15a` all roots of `x^5-a_0x^4+3ax^3+bx^2+cx+d=0` can't be real. It is given that `a_0 ,a,b,c,d, in R`.

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PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. lim(x to 0) (1-cosx)/x^2 = ?

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  2. If f(x)=ax^3+bx^2+cx+d has local extrema at two points of opposite si...

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  3. Prove that if 2a0^2lt15a all roots of x^5-a0x^4+3ax^3+bx^2+cx+d=0 can...

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  4. Let a,b,c be real. If ax^2+bx+c=0 has two real roots alpha,beta where ...

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  5. Let a+b=4, where a gt 2 and let g(x)be a differentiable function. If ...

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  6. On the curve x^3=12y the abscissa changes at a faster rate than the or...

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  7. A spherical iron ball 10 cm in radius is coated with a layer of ice of...

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  8. The function f(x)=tan^(-1)x-x decreases in the interval

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  9. The function f(x)=2log(x-2)-x^2+4x+1 increases in the interval

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  10. The function f(x)=sin^4x+cos^4x increasing if :

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  11. The length of the longest interval in which the function 3sinx-4sin^3x...

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  12. The function f(x) =tan^(-1)(sinx+cosx) is an increasing function in

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  13. The function f defined by f(x)=4x^4-2x+1 is increasing for

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  14. The value of a for which the functionf(x)=asinx+1/3sin3x has an extrem...

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  15. xgt0,ygt0 and x+y=1. The minimum value of xlogx+ylogy is

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  16. The minimum value of 2log10x-logx0.01. xgt1, is

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  17. The maximum slope of the curve y=-x^3+3x^2+2x-27 is

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  18. For the function f(x)=xe^x, the point

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