Solving Quadratic Equations Flashcards

All 8 cards in this deck

What are the steps to solve a quadratic equation by factorising into two brackets?

e.g. $x^2 + 5x + 6 = 0$

1. Factorise into two brackets: $(x + 2)(x + 3) = 0$
2. Set each bracket equal to $0$: $x + 2 = 0$ or $x + 3 = 0$
3. Solve each: $x = -2$ and $x = -3$

True or false? To estimate the solutions of $x^2 - 4x + 2 = 0$ from a drawn graph of $y = x^2 - 4x + 2$, you read where the curve crosses the $y$-axis.

False. You read the $x$-values where the curve crosses the $x$-axis (where $y = 0$).

What are the solutions of an equation of the form $x^2 = k$, where $k$ is positive?

e.g. $x^2 = 36$

$x = \pm\sqrt{k}$ — two solutions, one positive and one negative.

e.g. $x = \pm 6$

Which method solves a quadratic equation with no number term?

e.g. $x^2 - 5x = 0$

Take out the common factor, then set each factor equal to $0$.

e.g. $x(x-5)=0$, so $x = 0$ or $x = 5$

True or false? $x^2 - 5x = 0$ can be solved by dividing both sides by $x$ to give $x = 5$.

False. Dividing by $x$ loses the solution $x = 0$; factorise to $x(x-5)=0$ to get both $x=0$ and $x=5$.

What are the steps to solve a quadratic equation that is not already equal to zero?

e.g. $x^2 + 3x = 10$

1. Move every term to one side so it equals $0$: $x^2 + 3x - 10 = 0$
2. Factorise: $(x+5)(x-2)=0$
3. Set each bracket to $0$: $x = -5$ or $x = 2$

Which line must you draw on the graph of $y = x^2 - x - 6$ to estimate the solutions of $x^2 - x - 6 = -2$, and what do you then read off?

Draw the line $y = -2$ and read the $x$-coordinates where the curve meets it.

True or false? To estimate the solutions of $x^2 - x = 4$ from a drawn graph of $y = x^2 - x$, you read the $x$-values where the curve meets the line $y = 4$.

True. The solutions are the $x$-coordinates of the intersections of the curve with $y = 4$.