Question

find the quadratic polynomial whose zeroes are 3+√5,3-√5

Answer 1

Answer:

Step-by-step explanation: Let 3+√5 be alpha and 3-√5 be beta, then

Alpha+beta=(3+√5)+(3-√5)

=3+√5+3-√5

=3+3

=6

Alpha×beta= (3+√5)(3-√5)

=3(3-√5)+√5(3-√5)

=9-3√5+3√5-5

=9-5

=4

According to quadratic formula,

x^2-(alpha+beta)x+alpha•beta=0

=> x^2-(6)x+(4)=0

=>x^2-6x+4=0

So, the quadratic polynomial is x^2-6x+4.

Answer 2

Answer:

zeros= 3+√5 and 3-√5

polynomial= x^2- (sum of zeros)x+ product of zeros

=x^2-(3+√5+3-√5)x + (3+√5)(3-√5)

= x^2 - 6x + 4

Hope it helps...