How do you find the zeros, real and imaginary, of y=x2+18x+81 using the quadratic formula?

1 Answer
Feb 11, 2017

We have only one zero x=9.

Explanation:

Zeros of a quadratic function y=f(x)=x2+18x+81 are those values of x for which y=0.

Using quadratic formula for a function f(x)=ax2+bx+c,

zeros are b±b24ac2a

and hence for y=f(x)=x2+18x+81,

zeros are 18±1824×1×812×1

i.e. 18±3243242=8±02=9

Check - We can write y=f(x)=x2+18x+81

= x2+2×9×x+92 - and using a2+2ab+b2=(a+b)2

= (x+9)2

and hence, y=0 only when x=9

Hence we have only one zero x=9.