itomath.com

Quadratic Equations

$x^2=k$ Null Factor Law Solving by Factorizing Problem Solving with Quadratics

Extension Problems

Solve for $𝑥$. If there are multiple answers, separate them with commas. Give answers as fractions and not decimals.

$\frac{3}{10000}x^2-\frac{7}{100}x+4=0$

$\left(x+3\right)^2=\frac{x+3}{2}+3$

$x^2-\left(\sqrt{2}+\sqrt{3}\right)x+\sqrt{6}=0$

$x^2-\left(a-2\right)x-2a=0$ (where $a$ is a constant)

$ax^2-\left(a+b\right)x+b=0$ (where $a$ and $b$ are constants)

$\left(a-1\right)x^2-\left(a^2-1\right)x=0$ (where $a$ is a constant)

The quadratic equation $x^2+2ax-3a=0$ has 2 solutions. One of the solutions is $x=-3$. Find $a$ and the other value of $x$.

$a=$

$x=$

If the quadratic equation $x^2-ax+24=0$ has 2 integer solutions, what is the minimum value of $a$? Assume $a$ is positive.

$a=$

The quadratic equation $x^2+2ax+a^2-4=0$ has 2 solutions. The difference between the two solutions is $4$ and one solution is $5$ times greater than the other solution. Given $a>0$, find the value of $a$ and the two values of $x$ (separate them with a comma).

$a=$

$x=$