Show that all the roots of the equation `a_(1)z^(3)+a_(2)z^(2)+a_(3)z+a_(4)=3,`
`(where|a_(i)|le1,i=1,2,3,4,)` lie
outside the circle with centre at origin and radius `2//3.`

What does a_(1) + a_(2) + a_(3) + …..+ a_(n) represent

Find the relation between acceleration of blocks a_(1), a_(2) and a_(3) .

Differentiate a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)+...+a_(n-1)x+a_(n)

If A_(1),A_(2),A_(3),………………,A_(n),a_(1),a_(2),a_(3),……a_(n),a,b,c epsilonR show that the roots of the equation (A_(1)^(2))/(x-a_(1))+(A_(2)^(2))/(x-a_(2))+(A_(3)^(2))/(x-a_(3))+…+(A_(n)^(2))/(x-a_(n)) =ab^(2)+c^(2) x+ac are real.

Show that for any real numbers a_(3),a_(4),a_(5),……….a_(85) , the roots of the equation a_(85)x^(85)+a_(84)x^(84)+……….+a_(3)x^(3)+3x^(2)+2x+1=0 are not real.

The displacement of a particle is given by x=a_(0)+(a_(1)t)/(3)-(a_(2)t^(2))/(2) where a_(0),a_(1) and a_(2) are constants. What is its acceleration ?

If the general solution of some differential equation is y=a_(1)(a_(2)+a_(3)).cos(x+a_(4))-a_(5)e^(x+a_(6)) then oder of differential equation is .....

If (a_(1),1,1),(1,a_(2),1) and (1,1,a_(3)) are coplaner (where a_(i)ge1,i=1,2,3) then underset(i=1)overset(3)sum(1)/(1-a_(i)) = …………..

Write the first five terms of the sequences in obtain the corresponding series: a_(1)= a_(2)= 1, a_(n)= a_(n-1) + a_(n-2), n gt 2

If a_(1),a_(2),a_(3),a_(4) and a_(5) are in AP with common difference ne 0, find the value of sum_(i=1)^(5)a_(i) " when " a_(3)=2 .