Question

For what real numbers x is the value of x2 – 6x + 9 negative

Answer 1

This is the concept of quadratic equations. The equation has the original form of y=ax^2+bx+c. Our equation is given by y=x^2-6x+9. Since our leading coefficient is positive, then it means that our function will not be negative at any point. In other words, the range is [0,∞). Hence we conclude that the function will be no where negative.

Answer 2

A real numbers are numbers that can be found on a number line, they include both rational and irrational numbers.
We can first solve the equation;
x² - 6x + 9 =0, using completing square method;
 x²- 6x + (-3)² = -9 + (-3)²
     (x-3)² = 0
       x = 3
therefore,  both values of x are 3, thus the expression has no real number x is negative.