Question 1

A quadratic equation is factorized into the for (2x + 3)(x + 4) = 0. Which option below is the equivalent equation in the form ax² + bx + c = 0? A) x² + 11x + 12 = 0 B) x² + 11x + 7 = 0 C) 2x² + 11x + 12 = 0 D) 2x² + 11x + 7 = 0

Accepted Answer

To find the equivalent equation in the form $ax^2 + bx + c = 0$, we need to expand the given factorized form: $(2x + 3)(x + 4) = 0$. Expanding this gives $2x^2 + 8x + 3x + 12 = 0$, which simplifies to $2x^2 + 11x + 12 = 0$.

Question 2

When a quadratic equation is solved graphically, which feature of the graph represents the solution(s) to the equation?&#10;A) The mean gradient of the curve&#10;B) The point(s) at which the graph crosses the vertical (y) axis&#10;C) The point(s) at which the graph crosses the horizontal (x) axis&#10;D) The area between the curve and the horizontal axis

Accepted Answer

The solutions to a quadratic equation, when solved graphically by plotting its corresponding quadratic function, are represented by the x-intercepts of the graph. These are the points where the graph crosses the horizontal (x) axis.

Question 3

What is the MAXIMUM number of solutions for a quadratic equation?&#10;A) 0&#10;B) 1&#10;C) 2&#10;D) 3

Accepted Answer

A quadratic equation can have a maximum of 2 solutions, as it is represented by the formula ax^2 + bx + c = 0, where a, b, and c are constants, and x represents the variable. The solutions are determined by the discriminant (b^2 - 4ac).

Question 4

What is the only solution for the equation y = -2x² + 4x - 2? A) x = -0.5 B) x = 0 C) x = 0.5 D) x = 1

Accepted Answer

The equation y = -2x^2 + 4x - 2 is a quadratic equation. To find the solution, set y to 0 and solve for x: 0 = -2x^2 + 4x - 2. Factoring or using the quadratic formula reveals that x = 1 is the only solution.

Question 5

Which is the correct form of a cubic equation when a = 3; b = -6; c = 2; d = 4? A) y = 3x³ + 6x² + 2x + 4 B) y = 3x³ - 6x² - 2x + 4 C) y = 3x³ + 6x² + 2x - 4 D) y = 3x³ - 6x² + 2x + 4

Accepted Answer

The correct form of a cubic equation is given by $y = ax^3 + bx^2 + cx + d$. Substituting the given values $a = 3$, $b = -6$, $c = 2$, and $d = 4$ into this formula, we get $y = 3x^3 - 6x^2 + 2x + 4$, which matches option D.

Question 6

What is the MAXIMUM number of solutions for a cubic equation?&#10;A) 1&#10;B) 2&#10;C) 3&#10;D) 4

Accepted Answer

A cubic equation, which is an equation of the form ax^3 + bx^2 + cx + d = 0, can have up to 3 real roots (solutions) according to the Fundamental Theorem of Algebra.

Question 7

The formula y = 2x² + 5x +2 has two solutions for x. One is x = -3.5. Find the other using the formula method. A) x = 1 B) x = 1.5 C) x = 2 D) x = 2.5

Accepted Answer

The quadratic formula x = [-b ± sqrt(b² - 4ac)] / 2a is used to find the roots. For y = 2x² + 5x + 2, a = 2, b = 5, c = 2. Using the formula, the solutions are x = [-5 ± sqrt(5² - 4*2*2)] / 4. This simplifies to x = [-5 ± sqrt(9)] / 4, giving x = -3.5 and x = 1.

Question 8

A quadratic equation is factorized into the form (x - 5)(x + 6) = 0. Which option below shows the correct pair of solutions for x?&#10;A) x = 5; x = -6&#10;B) x = 5; x = 6&#10;C) x = -5; x = -6&#10;D) x = -5; x = 6

Accepted Answer

Setting each factor equal to zero gives the solutions x = 5 and x = -6.

Question 9

What is the maximum power of a variable in a quadratic equation?&#10;A) 1&#10;B) 2&#10;C) 3&#10;D) 4

Accepted Answer

The maximum power of a variable in a quadratic equation is 2, as it is defined by the general form ax^2 + bx + c = 0, where x^2 represents the highest power of the variable.

Question 10

Which of the following options represents a quadratic equation when a = 3, b = -3 and c = 4? A) y = 3x² + 3x +4 B) y = 3x² - 3x - 4 C) y = 3x² - 3x + 4 D) y = 3x² + 3x - 4

Accepted Answer

The general form of a quadratic equation is $ax^2 + bx + c$. Given $a = 3$, $b = -3$, and $c = 4$, the correct equation is $y = 3x^2 - 3x + 4$.

Deck 26: Quadratic and Cubic Equations