Question

If a + rootb and a-rootb are the zeroes of a polynomial, then find the
polynomial,​

Answer 1

Answer:

0

Step-by-step explanation:

Any number multiplied with it becomes 0.

Answer 2

If a + rootb and a-rootb are the zeroes of a polynomial, then the  polynomial is $x^{2} -2ax+(a^{2} -b)$

Step-by-step explanation:

Given $a+\sqrt{b} ,   a-\sqrt{b}$ are two zeros of the polynomial.

Sum of zeros is $\alpha +\beta =(a+\sqrt{b} )+(a-\sqrt{b} )$

                         $\alpha +\beta =2a$

Product of zeros is $\alpha \beta =(a+\sqrt{b} )(a-\sqrt{b} )$

                      $\alpha \beta =a^{2} -(\sqrt{b} )^{2}$

                      $\alpha \beta =a^{2} -b$

Now polynomial is $x^{2} -(\alpha +\beta )x+\alpha \beta$

                              $=x^{2} -2a\times x+(a^{2} -b)$

So polynomial is $x^{2} -2ax+(a^{2} -b)$