Question

if alpa and beta are zeroes of x2-2root2x-6, find the quadratic polynomial q(x) whose zeroes are 1/a and 1/b

Answer 1

QUADRATIC Polynomia can be written as

X2-(a+b)X +ab

a is the 1st zero

b is the 2nd zero

so sum of zeroes 1/a+1/b =a+b/ab

So comparing with Ist Quadratic polynomial

so atb= 2root 2

ab =-6

so putting the values

a+b/ab=2root2/-6= root 2/3

• 1/a×1/b= 1/ab
• =1/-6 =-6

so quadratic polynomial q(x)is

=X2-(root2/3)X+(-6)

=X2-(root2/3)X-6