Part BConsider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, which statement is true about the other zero? A. The other zero must be rational. B. The other zero must be irrational. C. The other zero can be either rational or irrational. D. The other zero must be non-real.
Question
Part BConsider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, which statement is true about the other zero? A. The other zero must be rational. B. The other zero must be irrational. C. The other zero can be either rational or irrational. D. The other zero must be non-real.
Solution
The correct answer is B. The other zero must be irrational. This is due to the Conjugate Root Theorem, which states that if a polynomial has rational coefficients and one root is a non-real complex number or an irrational number, then its conjugate must also be a root. In this case, if one root of a quadratic equation is irrational, then the other root must also be irrational.
Similar Questions
Given:(1) The following argument is valid:p -> qNOT p______Therefore NOT q(2) Let a and b be two positive integers such that a > 1, b > 1, and a > b.SQRT(SQRT(a)) - SQRT(SQRT(b)) is always an irrational number.Select one of the following choices:Question 1Answera.(1) and (2) are False.b.(1) and (2) are True.c.(1) is True and (2) is False.d.(1) is False and (2) is True.
Which statement is TRUE? a. All integers are whole numbers. b. All integers are rational numbers. c. Irrational numbers are not real numbers. d. All rational numbers are integers.
Identify the true statement.A quadratic equation is of the form , where , , and are constants and .A quadratic equation is of the form , where and are non-zero constants.A quadratic equation is of the form , where , , and are constants and .A quadratic equation is of the form , where , , and are non-zero
If a quadratic equation has a discriminant that equals zero, which of the following statements is always true?
The product of any two irrational numbers is(A) always an irrational number(B) always a rational number(C) always an integer
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.