Question Type 4: Finding roots of quadratics by converting into a(x-p)(x-q) and equating to 0 Exercises

The profit $P(x)$ (in thousands of dollars) of a company is modeled by $P(x) = -x^2 + 5x + 14$, where $x$ represents thousands of units sold. Express this quadratic in factorized form and hence determine the values of $x$ for which $P(x) = 0$.

Determine all integer values of $k$ for which the equation $2x^2 + kx + 8 = 0$ has integer roots, by expressing it as $2(x - p)(x - q) = 0$.

Convert the quadratic $2x^2 - 10x + 12$ into the form $2(x - p)(x - q)$ and hence find its roots.

Solve $5x^2 + 20x + 15 = 0$ by writing it as $5(x - p)(x - q) = 0$.

Express $3x^2 - 2x - 8 = 0$ in the form $3(x - p)(x - q) = 0$ and find its solutions.

Solve $x^2 + x - 6 = 0$ by rewriting it as $(x - p)(x - q) = 0$.

Find the roots of $3x^2 + 2x - 8 = 0$ by expressing it in the form $3(x - p)(x - q) = 0$.

Find the roots of the quadratic equation $x^2 - 5x + 6 = 0$ by expressing it in the form $(x - p)(x - q) = 0$.

Find the roots of $6x^2 - x - 2 = 0$ by converting it into the form $6(x - p)(x - q) = 0$.

Determine the roots of $x^2 - 9x + 20 = 0$ by expressing it in the form $(x - p)(x - q) = 0$.

Express $4x^2 - 4x - 8 = 0$ in the form $4(x - p)(x - q) = 0$ and find $x$.

Solve the equation $2x^2 + x - 3 = 0$ by rewriting it as $2(x - p)(x - q) = 0$.