Quadratic Equations with Rational, Irrational, Complex Roots

A teacher asked their students to find the solutions of the equation 2x²+4x+3=0. Which student is correct?

• Jason

• Andrew

• Matthew

• Jacob

Select all equations that have two solutions.

Mathematical Equivalence

ON

• The equation has no solutions.

• The equation has one solution: 5.

• The equation has two solutions: -2 and 0.

• The equation has infinitely many solutions.

Solve using the quadratic formula.
2x² - 9x - 35 = 0

• x = 7/2, x = -6

• x = -5/2, x =5

• x = -3/7, x =6

• x = -5/2, x = 7

The discriminant is

• ax² + bx + c

• b - 4ac

• b² - 4ac

• b² + 4ac

Solve using the Quadratic Formula

6x² - 52 = 11x

• x = 4, -2.17

• x = -4, 2.17

• x = -3.71, -1.88

• x = 3.71, 1.88

If the discriminant is negative, then the quadratic has:

• 1 Rational Solution

• 2 Rational Solutions

• 2 Irrational Solutions

• 2 Complex Solutions

The quadratic equation can be used to solve quadratic equations that cannot be factored.

• True

• False

Solve x² - 5x + 10 = 0

• (5 - i√15)/2  ,  (5 + i√15)/2

• (5 - √15)/2  ,  (5 + √15)/2

• (5 - i√65)/2  ,  (5 + i√65)/2

• (5 - √65)/2  ,  (5 + √65)/2