Form the quadratic equation in the form $x^{2} + b x + c = 0$ whose roots are $4$ and $- 7$ .

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Solve the quadratic equation $2 x^{2} - 5 x - 3 = 0$ .
Determine the maximum value of the quadratic function $f (x) = - 2 x^{2} + 8 x - 3$ .
Find the equation of the axis of symmetry for the quadratic curve $f (x) = x^{2} - 6 x + 5$ .
Find the values of $k$ if the quadratic equation $x^{2} + k x + 9 = 0$ has two equal real roots.
Solve the equation $(x - 2) (x + 3) = 14$ .
A rectangular school garden has a length of $(x + 4) m$ and a width of $(x - 2) m$ . Given that the total area of the garden is…