Nature of Solutions

The discriminant is...

• ax² + bx + c

• b² + 4ac

• b² - 4ac

• b - 4ac

If the discriminant is equal to -7 the roots will be...

• Real, rational & equal

• Real, rational & different

• Real, irrational & different

• Non-real & different

If the discriminant is equal to 0 the roots will be...

• Real, rational & equal

• Real, rational & different

• Real, irrational & different

• Non-real & different

If the discriminant is equal to 49 the roots will be...

• Real, rational & equal

• Real, rational & different

• Real, irrational & different

• Non-real & different

Select the letters that identify whether each equation has no solution, one solution, or infinitely many solutions. Only 1 letter corresponds to each equation.

• A, E, I

• B, D, G

• B, F, H

• C, D, H

The roots of 4x² - 1 = 0 will be

• Real, rational & equal

• Real, rational & different

• Real, irrational & different

• Non-real & different

The roots of x² + 35x = 105 will be

• Real, rational & equal

• Real, rational & different

• Real, irrational & different

• Non-real & different

Determine the value of the discriminant and name the nature of the solution for the following:

x² + 2x - 63

• 256 - 2 different, Real & Rational roots

• √(-256) - 2 different non-Real roots

• √(137) - 2 different Real & Irrational roots

• 123 - 2 different Real & Rational roots

If the discriminant of f(x) is 0, the graph of y = f(x) has

• x-intercept

• x-intercepts

• 0 x-intercepts

• It's impossible to tell

If the discriminant of f(x) is -12, the graph of y = f(x) has

• x-intercept

• 2 x-intercepts

• 0 x-intercepts

• It's impossible to tell