If the polynomial `(a^(2)-b^(2))x^(2)+2abx+(a^(2)+b^(2))a,b,c` are constants, be a linear polynomial, then prove that a = b.

If the polynomial (a^(2)+b^(2)+c^(2)-ab-bc-ca)x^(2)+2abcx+(a^(2)+b^(2)+c^(2)) , where a, b, c are constants, be a linear polynomial, then prove that a = b = c.

(a+b)^(2)x^(2)-4abx-(a-b)^(2)=0

If alpha and beta are zeroes of the quadratic polynomial 2x^(2)+2(a+b)x+a^(2)+b^(2) , form the quadratic polynomial whose zeroes are (alpha+beta)^(2) .

If -2 is a zero of the polynomial ax^(3)+bx^(2)+x-b and the value of the polynomial is 4 at x=2 then find the values of a and b.

sqrt(a^(2)x^(2)+2abx+b^(2)) = ……………..

Find the LCM of the polynomials ab(x^(2)+1)+x(a^(2)+b^(2)) and ab(x^(2)-1)+x(a^(2)-b^(2))

In the polynomial p(x)= a x^ 3 + b x^ 2 + c x + d if p(2)=p(-2), prove that 4a+c=0.

The roots of a^(2)x^(2)+abx+b^(2),ane0 are :

If a,b,c,x are all real numbers,and (a^(2)+b^(2))x^(2)-2b(a+c)x+(b^(2)+c^(2))=0 prove that a,b,c are in G.P.,and x is their common ratio.