Question

if one zero of f(x)=(b^2+4)x^2+13x+4b is reciprocal of other. find b

Answer 1

Let one zero be x..Then the other zero will be 1/x.

Given Equation is (b^2 + 4)x^2 + 13x + 4b.

It is in the form of ax^2 + bx + c = 0,

Where a = (b^2 + 4), b = 13, c = 4.

Now,

We know that product of zeroes = c/a

x * 1/x = 4b/(b^2 + 4)

1 = 4b/b^2 + 4

b^2 + 4 = 4b

b^2 - 4b + 4 = 0

(b - 2)^2 = 0

b = 2.


Therefore the value of b = 2.


Hope this helps!