Show that the following equation can have at most one real root `3x^5-5x^3+21x+3sinx+4cosx+5=0`

Find whether the following equation have real roots. If real roots exist, find them 3x^2-4x+5=0

Prove that the equation 3x^(5)+15x -8=0 has only one real root .

Show that the equation x^(2)+5x-6=0 has real roots.

Find whether the following equations have real roots. If real roots exist, find them 5x^(2)-2x-10=0

Find whether the following equations have real roots. If real roots exist, find them 5x^(2)-6x-2=0

Show that the equation x^(5)+5x+a=0 cannot have more than one real root for any real value of a.

Find whether the following equations have real roots. If real roots exist, find them 1/(2x-3)+1/(x-5)=1,x!=3/2,5

Find whether the following equations have real roots. If real roots exist, find them x^(2)+5sqrt(5)x-70=0

Show that the equation x^(5)-3x-1=0 has a unique root in [1,2] .

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them : 2x^(2) - 3x + 5 = 0