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Frame a quadratic polynomial p(x) whose sum of zeroes is -3 and product of zeroes is -2/3?
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Frame a quadratic polynomial p(x) whose sum of zeroes is -3 and produc...
Quadratic Polynomial with Sum and Product of Zeroes


To frame a quadratic polynomial whose sum of zeroes is -3 and product of zeroes is -2/3, we need to follow certain steps:




  • Step 1: Write the Quadratic Polynomial

    Let p(x) be the quadratic polynomial we need to frame. Then, we can write:

    p(x) = ax2 + bx + c



  • Step 2: Use the Sum and Product of Zeroes to Form Equations

    Using the sum and product of zeroes, we can form the following equations:

    α + β = -3

    α × β = -2/3

    Here, α and β are the zeroes of the polynomial.



  • Step 3: Express the Coefficients in terms of α and β

    Using the equations from step 2, we can express the coefficients a, b, and c in terms of α and β:

    a = 1

    b = -α - β

    c = α × β



  • Step 4: Substitute the Coefficients in the Quadratic Polynomial

    Substituting the coefficients from step 3 in the quadratic polynomial from step 1, we get:

    p(x) = x2 - (-α - β)x + α × β

    p(x) = x2 + (α + β)x - α × β

    Now, substituting the values of α and β from step 2, we get:

    p(x) = x2 - 3x - (-2/3)

    p(x) = x2 - 3x + 2/3




Therefore, the quadratic polynomial with sum of zeroes as -3 and product of zeroes as -2/3 is p(x) = x2 - 3x + 2/3.
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Frame a quadratic polynomial p(x) whose sum of zeroes is -3 and product of zeroes is -2/3?
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Frame a quadratic polynomial p(x) whose sum of zeroes is -3 and product of zeroes is -2/3? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Frame a quadratic polynomial p(x) whose sum of zeroes is -3 and product of zeroes is -2/3? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Frame a quadratic polynomial p(x) whose sum of zeroes is -3 and product of zeroes is -2/3?.
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