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  2. Division by zero - Wikipedia

    en.wikipedia.org/wiki/Division_by_zero

    A positive or negative number when divided by zero is a fraction with the zero as denominator. Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero. In 830, Mahāvīra unsuccessfully tried to correct the mistake ...

  3. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    The roots of the quadratic function y = ⁠ 1 / 2 ⁠ x 2 − 3x + ⁠ 5 / 2 ⁠ are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.

  4. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    Because (a + 1) 2 = a, a + 1 is the unique solution of the quadratic equation x 2 + a = 0. On the other hand, the polynomial x 2 + ax + 1 is irreducible over F 4, but it splits over F 16, where it has the two roots ab and ab + a, where b is a root of x 2 + x + a in F 16. This is a special case of Artin–Schreier theory.

  5. Extraneous and missing solutions - Wikipedia

    en.wikipedia.org/wiki/Extraneous_and_missing...

    The problem is that we divided both sides by , which involves the indeterminate operation of dividing by zero when = It is generally possible (and advisable) to avoid dividing by any expression that can be zero; however, where this is necessary, it is sufficient to ensure that any values of the variables that make it zero also fail to satisfy ...

  6. Quadratic function - Wikipedia

    en.wikipedia.org/wiki/Quadratic_function

    In mathematics, a quadratic function of a single variable is a function of the form [1] = + +,,where ⁠ ⁠ is its variable, and ⁠ ⁠, ⁠ ⁠, and ⁠ ⁠ are coefficients.The expression ⁠ + + ⁠, especially when treated as an object in itself rather than as a function, is a quadratic polynomial, a polynomial of degree two.

  7. Quartic equation - Wikipedia

    en.wikipedia.org/wiki/Quartic_equation

    In either case the full quartic can then be divided by the factor (x − 1) or (x + 1) respectively yielding a new cubic polynomial, which can be solved to find the quartic's other roots. If a 1 = a 0 k , {\displaystyle \ a_{1}=a_{0}k\ ,} a 2 = 0 {\displaystyle \ a_{2}=0\ } and a 4 = a 3 k , {\displaystyle \ a_{4}=a_{3}k\ ,} then x = − k ...

  8. Polynomial long division - Wikipedia

    en.wikipedia.org/wiki/Polynomial_long_division

    Divide the first term of the dividend by the highest term of the divisor (x 3 ÷ x = x 2). Place the result below the bar. x 3 has been divided leaving no remainder, and can therefore be marked as used by crossing it out. The result x 2 is then multiplied by the second term in the divisor −3 = −3x 2. Determine the partial remainder by ...

  9. Indeterminate form - Wikipedia

    en.wikipedia.org/wiki/Indeterminate_form

    Indeterminate form is a mathematical expression that can obtain any value depending on circumstances. In calculus, it is usually possible to compute the limit of the sum, difference, product, quotient or power of two functions by taking the corresponding combination of the separate limits of each respective function.