Question

Determine whether the statement is always, sometimes, or never true:

A quadratic function with real coefficients has real zeros.

Answer 1

The statement 'A quadratic function with real coefficients has real roots' is some times true and some times false.

Explanation:

The quadratic function in the form ax² + bx + c = 0, has real roots when the discriminant, given by D = b² - 4ac is greater than or equal to zero.

And the equation has imaginary roots when D = b² - 4ac is less than zero.

So, even a quadratic equation has real coefficients can have non-real roots depending on the value of the discriminant.

Hence, the statement 'A quadratic function with real coefficients has real roots' is some times true and some times false. (Answer)