Sridharacharya Method |Quadratic Equation | Class 9 | ICSE | CBSE

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The quadratic formula, x equal to minus b plus minus root over b square minus 4ac upon 2a, is essential for solving quadratic equations and is credited to the Indian mathematician Sridaracharaya, providing two solutions for x. Specifically, applying the quadratic formula to a quadratic equation with coefficients 2, 5, and -6 results in x equal to -5 plus minus root over 73 by 4, giving the two solutions for x.

Insights

  • The general form of a quadratic equation is ax^2 + bx + c = 0, where a cannot be 0 to maintain the quadratic nature.
  • The quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a, is essential for solving quadratic equations and was developed by the Indian mathematician Sridaracharaya.

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Recent questions

  • What is the general form of a quadratic equation?

    The general form of a quadratic equation is ax^2 + bx + c = 0, where 'a' cannot be 0.

  • How can the method of completing the square be applied?

    The method of completing the square can be applied by dividing the equation by 'a' or multiplying the equation by 'a' to create a perfect square.

  • What is the quadratic formula?

    The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a, crucial for solving quadratic equations.

  • Who is credited with the quadratic formula?

    The quadratic formula is attributed to the Indian mathematician Sridaracharaya.

  • How are the solutions of a quadratic equation calculated?

    The solutions of a quadratic equation can be calculated using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a.

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Summary

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Quadratic Equation: Completing the Square and Formula

  • The general form of a quadratic equation is a x square plus b x plus c equal to 0, where a cannot be 0 to maintain the quadratic nature.
  • The method of completing the square can be applied in two ways: dividing the equation by a or multiplying the equation by a to create a perfect square.
  • By dividing the equation by a, x square plus b by a into x equals negative c by a, leading to x plus b by 2a whole square on the left side.
  • Taking the square root of both sides after simplification results in x equal to negative b by 2a plus minus root over b square minus 4ac by 2a.
  • Multiplying the entire equation by a, simplifying, and taking the square root yields x equal to negative b plus minus root over b square minus 4ac by 2a.
  • The quadratic formula, x equal to minus b plus minus root over b square minus 4ac upon 2a, is crucial for solving quadratic equations and is attributed to the Indian mathematician Sridaracharaya.
  • Applying the quadratic formula to a specific quadratic equation with coefficients 2, 5, and -6 results in x equal to -5 plus minus root over 73 by 4, providing the two solutions for x.
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