Use the Discriminant to Determine Whether the Given Equation Has

question 92

Multiple Choice

Use the discriminant to determine whether the given equation has two irrational roots, two rational roots, one repeated root, or two complex roots. Do not solve. x² + 3 = 7x

• A) two irrational roots
• B) two rational roots
• C) one repeated root
• D) two complex roots

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Definitions:

Truth Table

A mathematical table used in logic to determine the veracity of various propositions under all possible scenarios.

Hypothetical Syllogism (HS)

A form of deductive reasoning that connects two conditional statements to arrive at a conclusion, if P then Q; if Q then R, therefore if P then R.

Modus Ponens (MP)

A valid form of argument where if a conditional statement ("if p then q") is accepted, and the antecedent (p) is true, then the consequent (q) must also be true.

Modus Tollens (MT)

A form of logical argument where, from "If P then Q" and "Not Q," it follows that "Not P."