Question

if one zero of the polynomial (m^2+3)x^2+23x+8 is the reciprocal of the other, find m

Answer 1

Answer:

m= positive root five and negative root five

Step-by-step explanation:

Using roots of quadratic equation, let us assume the roots as 1/x and x.

(m^2+3)x^2+23x+8

ax^2+bx+c=0

a=m^2+3

b=23

c=8

Therefore Sum of roots=(-b)/a

So, x+1/x=(x^2+1)/x  =  -(23)/(m^2+3)

Product of zeroes are c/a

=x*(1/x)=1=8/(m^2+3)

m^2+3=8

m^2=5

m=positive root five and negative root five.