quadratic equation with real roots example - Search
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  1. Roots of Quadratic Equation - Formula, How to Find, …

    • Then the above formula becomes, x = (-b ± √positive number )/2a and it gives us two real and different roots. Thus, the quadratic equation has two real and different roots when b2- 4ac > 0.… See more

    Nature of Roots When D < 0

    Then the above formula becomes, x = (-b ± √negative number )/2a and it gives us two complex roots (which are different) as the square root of a negative number is a complex nu… See more

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    Nature of Roots When D = 0

    Then the above formula becomes, x = (-b ± √0)/2a = -b/2a and hence the equation has only one real root. Thus, the quadratic equation has only one real root (or two equal root… See more

    Cuemath
    Sum of Roots of Quadratic Equation

    The sum of the roots = x1 + x2 = (-b + √ (b2 - 4ac)) /2a + (-b - √ (b2- 4ac) )/2a = -b/2a - b/2a = -2b/2a = -b/a Therefore, the sum of the roots of the quadratic equation ax2+ bx + c = 0 is -… See more

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    Product of Roots of Quadratic Equation

    The product of the roots = x1 · x2 = (-b + √(b² - 4ac) )/2a · (-b - √(b² - 4ac))/2a = (-b/2a)2 - ( √ (b2 - 4ac)/ 2a)2 ( by a² - b² formula) = b2 / 4a2 - (b2 - 4ac) / 4a2 = (b2 / 4a2) - (b2 / … See more

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  2. quadratic equation with real roots example

    Organizing and summarizing search results for you
    A quadratic equation with real roots has two solutions that are real numbers. Examples of quadratic equations with real roots include:
    • 3x^2 + 2x - 2 = 0 (roots: -1 and 2)
    • 3x^2 - 10x - 8 = 0 (roots: -2/3 and 4)
    • x^2 - 7x + 10 = 0 (roots: 2 and 5)
     
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  4. Nature of Roots of Quadratic Equation | Real and …

    Jul 31, 2017 · Learn how to determine whether a quadratic equation has real or complex roots based on the discriminant D. See examples of quadratic equations with real and complex roots and their solutions.

     
  5. Nature of Roots: Discriminant, Various Cases for D, …

    Learn how to determine the nature of roots of a quadratic equation based on the discriminant, which is b 2 - 4ac. See examples of different cases and types of roots, such as real, equal, unequal, rational, irrational, and imaginary.

  6. Nature of Roots of Quadratic Equations: Formulas …

    Apr 24, 2024 · When the discriminant (D) of a quadratic equation is a perfect square (the square of a rational number), the equation has rational (real) roots. Example: If D = 25, which is 5 2, it's a perfect square discriminant. The …

  7. Explain Real Roots with Examples. - GeeksforGeeks

  8. Quadratic Equation | Roots, Formula and Examples

    Dec 13, 2024 · A quadratic equation is a second-degree polynomial of the form ax\u00b2 + bx + c = 0, with solutions known as roots that can be found using various methods, and the nature of these roots is determined by the …

  9. Finding Roots of Quadratic (Equation, Examples

    Learn how to use the quadratic formula to find the roots of a quadratic equation, which are the values of x that make the equation zero. See examples of different types of roots, such as real, repeated, and complex roots, and how to graph …

  10. When Does A Quadratic Have Real Roots? (3 Ways …

    A quadratic equation has real roots when the discriminant is positive or zero (not negative). From an algebra standpoint, this means b2 >= 4ac. Visually, this means the graph of the quadratic (a parabola) touches the x axis at least once.

  11. Quadratic Equation. Roots & Methods to Solve with Examples

  12. Quadratic Equation- Definition, Rules, Examples,

    Aug 3, 2023 · Some examples of quadratic equations are: x 2 + 2x – 15 = 0, here a = 1, b = 2, and c =-15. x 2 – 49x = 0, here a = 1, b = -49, and c = 0. Sometimes the quadratic equations are outside the standard form and are …

  13. Roots of a Quadratic Equation - Math Only Math

  14. Nature of Roots of a Quadratic Equation: Formula, Examples

  15. Roots of Quadratic Equation: Definition, Formula and Examples

  16. Explain real roots with examples? - Vedantu

  17. Real World Examples of Quadratic Equations - Math is Fun

  18. Quadratic formula – Explanation & Examples - The Story of …

  19. 20 Quadratic Equation Examples with Answers - Neurochispas

  20. Roots of Quadratic Equation with Formula - Math Monks

  21. Nature of Roots of Quadratic Equations: Formulas and Examples