Question

If a & ß are the zeros of p(x) = x² + px +q, then a
polynomial having 1/a & 1/ß as its zeros is​

Answer 1

Given ,

• p(x) = x² + px + q
• p(x) = x² + px + q Roots = a & ß

Now, Sum of roots = -p/1

→ a + ß = -p

Product of roots = q/1

→ aß = q

Now,

★ 1/a + 1/ß

= a + ß/aß

= -p/q

★ 1/a × 1/ß

= 1/aß

= 1/q

So, the p(x) having 1/a & 1/ß as its zeros is

x ² -( 1/a + 1/ß)x + ( 1/a × 1/ß)

= x² + p/q . x + 1/q

= qx² + px + 1