+0

# Determining Validity of Conjectures

0
35
1

Determine whether the conjecture below is sometimes, always, or never true. Explain.

In a quadratic in standard form, if a and c are different signs, then the solutions will be real.

Guest Dec 3, 2017

#1
+1493
+2

Let's consider the discriminant of a quadratic, \(b^2-4ac\)

If and are opposite signs, then ac will be negative. -4ac will be positive, then. bwill also be positive--no matter whether b is positive or negative. This means that b2-4ac represents the addition of positive values, which will never be negative. Hence, the discriminant will always be positive, so the solutions can never be imaginary. This conjecture is always true.

TheXSquaredFactor  Dec 3, 2017
Sort:

#1
+1493
+2

Let's consider the discriminant of a quadratic, \(b^2-4ac\)

If and are opposite signs, then ac will be negative. -4ac will be positive, then. bwill also be positive--no matter whether b is positive or negative. This means that b2-4ac represents the addition of positive values, which will never be negative. Hence, the discriminant will always be positive, so the solutions can never be imaginary. This conjecture is always true.

TheXSquaredFactor  Dec 3, 2017

### 15 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details