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

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

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

Let f(x) = a_(0)x^(n) + a_(1)x^(n-1) + a_(2) x^(n-2) + …. + a_(n-1)x + a_(n) , where a_(0), a_(1), a_(2),...., a_(n) are real numbers. If f(x) is divided by (ax - b), then the remainder is

Differentiate the following with respect of x:a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)++a_(n-1)x+a_(n)

Let f(x)=a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)+......+a_(n),(a_(0)!=0) if a_(0)+a_(1)+a+_(2)+......+a_(n)=0 then the root of f(x) is

Let (a_(0))/(n+1)+(a_(1))/(n)+(a_(2))/(n-1)+...+(a_(n-1))/(2)+a_(n)=0 Show that there exists at least real x between 0 and 1 such that a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)+...+a_(n)=0

If p(x)=a_(n)x^(n)+a_(n-1)x^(n-1)+a_(n-2)x^(n-2)+.............+a_(1)x+a_(0) where n is a whole number and a_(0),a_(1),a_(2),……………,a_(n)(a_(n)ne0) are all constants, then p(0) =

If (a_(0))/(n+1) + ( a_(1))/( n ) + ( a_(2))/( n -1)+"......"+ (a_(n-1))/(2) + a_(n) =0 then a_(0)x^(n) + a_(1) x^(n-1) + "..........." + a_(n-1)x + a_(n) =0 has

a_(0)x^(n) + a_(1)x^(n-1) + a_(2)x^(n-2) + ……..a_(n)x^(n) is polynomial of degree ……………

If the equation a_(n) x^(n) + a_(n -1) x^(n-1) + .... + a_(1) x = 0, a_(1) ne 0, n ge 2 , has a positive root x = alpha , then the equation n a_(n) x^(n-1) + (n - 1) a_(n-1) x^(n-1) + ..... , a_(1) = 0 has a positive root, which is :