Amath Discriminant

For y = ax^2 + bx + c to be always positive, what are the criteria?

• a>0

• a<0

• b^2 - 4ac < 0

• b^2 - 4ac > 0

For y = ax^2 + bx + c to be always negative, what are the criteria?

• a > 0

• a < 0

• b^2 - 4ac < 0

• b^2 - 4ac > 0

For y = ax^2 + bx + c to be never negative, what are the possible criteria?

• a > 0

• a < 0

• b^2 - 4ac > 0

• b^2 - 4ac < 0

• b^2 - 4ac = 0

For y = ax^2 + bx + c to be never positive, what are the possible criteria?

• a < 0

• a > 0

• b^2 - 4ac > 0

• b^2 - 4ac < 0

• b^2 - 4ac = 0

Given a quadratic equation, ax^2 + bx + c = 0, when b^2 - 4ac > 0, the possible scenario(s) may occur

• There are 2 real and distinct roots

• There is only 1 real root

• There is no real root

Given that (x + 3)(x + 5) > 0, what is the range of values of x? You may choose 1 or more answers.

• x > -3

• x > -5

• -5 < x < 3

• x < -5 and x > -3

Given that -2(x - 4)(x + 5) < 0, what are the range of values of x? You may choose 1 or more than 1 answers.

• -5 < x < 4

• x < 4

• x < -5

• x < -5 or x > 4

Which of the following is the first step in solving quadratic inequalities?

• Make RHS of the inequality zero by bringing all the items to LHS

• Factorise the LHS

• Sketch quadratic curve to determine the solution