Quadratic Equations

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A quadratic equation in variable x is an equation of the form ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0. This is called the standard form of a quadratic equation. The polynomial ax² +…

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A real number α is called a root of the quadratic equation ax² + bx + c = 0 if aα² + bα + c = 0. We also say that x = α is a solution of the quadratic equation, or α satisfies the quadratic equation.

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Yes, x² - 6x + 8 = 0 is a quadratic equation because it is in the form ax² + bx + c = 0 where the coefficient of x² is non-zero. Here: a = 1, b = -6, c = 8.

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To factor 2x² - 5x + 3 = 0, we need p and q such that p + q = -5 and p × q = 2 × 3 = 6. The pair (-2, -3) works. So: 2x² - 2x - 3x + 3 = 2x(x - 1) - 3(x - 1) = (2x - 3)(x - 1) = 0. Therefore, x = 3/2 …

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1. Write the equation in standard form ax² + bx + c = 0 2. Find two numbers p and q such that p + q = b and p × q = ac 3. Split the middle term: ax² + px + qx + c = 0 4. Factor by grouping 5. Set each…

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Completing the square is a method where we adjust the left side of the quadratic equation to make it a perfect square of a linear polynomial. It's used when factorisation is difficult or impossible. T…

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x² + 4x - 4 = 0 ⇒ x² + 4x = 4 ⇒ x² + 2(x)(2) + 2² = 4 + 4 ⇒ (x + 2)² = 8 ⇒ x + 2 = ±√8 = ±2√2 ⇒ x = -2 ± 2√2…

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The quadratic formula is: x = (-b ± √(b² - 4ac))/2a, where ax² + bx + c = 0 (a ≠ 0). This formula can be used to find the roots of any quadratic equation, especially when factorisation is not possible…