Quadratic Equations with Irrational Solutions

Choose the nature of the solutions for a quadratic equation with the following discriminant.

Discriminant = 18

• 2 complex solutions

• 2 real, rational solutions

• 2 real, irrational solutions

• 1 real, rational solution

• 1 complex solution

If D > 0 but not a perfect square, the quadratic equation is said to have 2 real solutions which are ______

• rational and unequal

• irrational and unequal

• 
  rational and equal/repeated

• imaginary and complex

Give the Nature of the Roots of a given Quadratic Equations with the following DISCRIMINANT:

D = 8

• The roots are RATIONAL AND EQUAL

• The roots are RATIONAL AND UNEQUAL

• The roots are IRRATIONAL AND EQUAL

• The roots are IRRATIONAL AND UNEQUAL

What is the formula for the discriminant?

• x = -b/2a

• b² - 4ac

• a² + b² = c²

• x = [-b±√(b²-4ac)]/2a

Is the answer to the quadratic below rational, irrational, or it is impossible to tell

(x-25)² = 22

• Rational

• Irrational

• Impossible to tell

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

The discriminant is

• ax² + bx + c

• b - 4ac

• b² - 4ac

• b² + 4ac

Solve for x:

3x² - 6x + 6 = 0

• x = 1± i

• x = 3, -6

• x = 4.8, 2.7

• Undefined

If the discriminant is positive but NOT a perfect square, then the quadratic has:

• 1 Rational Solution

• 2 Irrational Solutions

• 2 Rational Solutions

• 2 Complex Solutions

How many solutions does the quadratic equation below have?

• No Real Roots

• 1 Rational Root

• 2 Rational Roots

• 2 Irrational Roots