Question

if(a-b) a(a+b)are the zeroes of polynomial x3-6x2+9x+5 the value of a is _​

Answer 1

Answer:

Given cubic polynomial is 

p(x)=x3−6x2+3x+10

The zeros of the polynomial p(x) are of the form a, a+b and a+2b 

Then,

   a+a+b+a+2b=−1−6

=>3a+3b=6

=>a+b=2     ----------------(i)

Also,  a(a+b)+(a+b)(a+2b)+a(a+2b)=13

=>a2+ab+a2+2ab+ab+2b2+a2+2ab=3

=>3a2+2b2+6ab=3  ----(ii)

and   a(a+b)(a+2b)=−1−10

=>a3+a2b+2a2b+2ab2=10

From (i), b=2−a

Putting this value in (ii), we get

Answer 2

Given cubic polynomial is 

p(x)=x3−6x2+3x+10

The zeros of the polynomial p(x) are of the form a, a+b and a+2b 

Then,

   a+a+b+a+2b=−1−6

=>3a+3b=6

=>a+b=2     ----------------(i)

Also,  a(a+b)+(a+b)(a+2b)+a(a+2b)=13

=>a2+ab+a2+2ab+ab+2b2+a2+2ab=3