Quadratic Equations

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A quadratic equation is an equation of the form ax² + bx + c = 0, where a ≠ 0 and a, b, c are real numbers. Here 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term…

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A quadratic polynomial is a polynomial of degree 2 in the form p(x) = ax² + bx + c, where a ≠ 0. Examples: (1) 5x² - 3x + 7, (2) 2x² - 9…

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A number α is called a root or solution of the quadratic equation ax² + bx + c = 0 if and only if aα² + bα + c = 0. In other words, when we substitute this value in the equation, it satisfies the equa…

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The quadratic formula is: x = (-b ± √(b² - 4ac))/2a. Here, a, b, c are coefficients of the quadratic equation ax² + bx + c = 0, and the expression (b² - 4ac) under the square root is called the discri…

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The discriminant is the expression b² - 4ac in the quadratic formula. It is denoted by D. For the equation ax² + bx + c = 0, D = b² - 4ac. The discriminant determines the nature of roots.

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If D = b² - 4ac > 0, then the quadratic equation has two real and distinct roots. The roots are different real numbers.

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If D = b² - 4ac = 0, then the quadratic equation has two equal real roots. Both roots have the same value, which is x = -b/2a.

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If D = b² - 4ac < 0, then the quadratic equation has no real roots. The equation cannot be satisfied by any real number.