Home
Class 12
MATHS
If the equation a0x^n +a1x^(n-1) +....a(...

If the equation `a_0x^n +a_1x^(n-1) +....a_(n-1)x=0` has a positive root `alpha` prove that the equation `na_0x^(n-1) +(n-1)a_1 x^(n-2) + ---+a_(n-1) = 0` also has a positive root smaller than `alpha`

Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that if the equation a_(0)x^(n)+a_(1)x^(n-1)+….+ a_(n-1) x = 0 has a positive root x_(0) , then the equation na_(0)x^(n-1) +(n-1) a_(1)x^(n-2) +….+ a_(n-1) =0 has a positive root less than x_(0) .

If the equation a_(n)x^(n)+a_(n-1)x^(n-1)+..+a_(1)x=0, a_(1)!=0, n ge2 , has a positive root x=alpha then the equation na_(n)x^(n-1)+(n-1)a_(n-1)x^(n-2)+….+a_(1)=0 has a positive root which is

If the equation a_(n)x^(n)+a_(n-1)x^(n-1)+..+a_(1)x=0, a_(1)!=0, n ge2 , has a positive root x=alpha then the equation na_(n)x^(n-1)+(n-1)a_(n-1)x^(n-2)+….+a_(1)=0 has a positive root which is

If the equation a_(n)x^(n)+a_(n-1)x^(n-1)+..+a_(1)x=0, a_(1)!=0, n ge2 , has a positive root x=alpha then the equation na_(n)x^(n-1)+(n-1)a_(n-1)x^(n-2)+….+a_(1)=0 has a positive root which is

If the equation a_(n)x^(n)+a_(n-1)x^(n-1)+..+a_(1)x=0, a_(1)!=0, n ge2 , has a positive root x=alpha then the equation na_(n)x^(n-1)+(n-1)a_(n-1)x^(n-2)+….+a_(1)=0 has a positive root which is

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 alpha , then the equation na_(n)x^(n-1)+(n-1)a_(n-1)x^(n-2)+ … +a_(1)=0 has a positive root, which is -

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 :

If the equation a_(n)x^(n) + a_(n-1) x^(n-1)+"......" + a_(1) x= 0 (a_(1) cancel(=)0,nge 2) has a positive root x = alpha then the equation na_(n) x^(n-1)+(n-1)a_(n-1)x^(n-2)+"......"+a_(1) =0 has a positive root, which is

If the polynomial equation a_n x^n + a_(n-1) x^(n-1) + a_(n-2) x^(n-2) + ....... + a_0 = 0, n being a positive integer, has two different real roots a and b . then between a and b the equation na_n x^(n-1) +(n-1)a_(n-1) x^(n-2) +.......+a_1 =0 has