Quadratic Equations and Inequalities

The video tutorial covers exam revision techniques focusing on solving quadratic equations, using the quadratic formula, and rounding to two decimal places. It also addresses solving equations with square roots, testing solutions, and solving quadratic inequalities using graphical methods. Additionally, the tutorial explains solving simultaneous equations for x and y.

What is the first step in solving a quadratic equation by equating brackets to zero?

• Expand the brackets

• Set each bracket equal to zero

• Multiply the brackets

• Add the brackets

If 3x + 4 = 0, what is the value of x?

• -3/4

• -4/3

• 4/3

• 3/4

Which method can be used to solve a quadratic equation to two decimal places?

• Quadratic formula

• Graphical method

• Substitution

• Trial and error

What is the quadratic formula used for solving equations?

• x = b ± √(b² + 4ac) / 2a

• x = b ± √(b² - 4ac) / 2a

• x = -b ± √(b² - 4ac) / 2a

• x = -b ± √(b² + 4ac) / 2a

How do you test if a solution is valid for an equation involving square roots?

• Confirm the solution is a fraction

• Verify the solution is an integer

• Ensure the solution is positive

• Check if both sides are equal after substitution

What is the result of squaring both sides of the equation √(2x + 7) = 4 - x?

• 2x + 7 = 16 - 8x + x²

• 2x + 7 = 4 - x

• 2x + 7 = 16 - x

• 2x + 7 = (4 - x)²

What is the graphical method used for solving quadratic inequalities?

• Graphical method

• Number line

• Substitution method

• Algebraic method

In the inequality x² - x - 56 < 0, what are the critical values?

• x = 7 and x = -8

• x = 8 and x = -7

• x = -7 and x = -8

• x = 7 and x = 8

How do you solve simultaneous equations with y as the subject?

• By graphing both equations

• By using the quadratic formula

• By substituting x into one equation

• By equating the expressions for y

What is the value of y when x = 12 in the equation y = 4x + 4?

• 48

• 52

• 56

• 60