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Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficient x*2 -5x + 6?
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Find the zeros of the following quadratic polynomials and verify the r...
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Find the zeros of the following quadratic polynomials and verify the r...
Finding Zeros of Quadratic Polynomials:

  • Quadratic polynomials are of the form ax^2 + bx + c.

  • To find the zeros, we need to set the polynomial equal to zero and solve for x.

  • In this case, the quadratic polynomial is x^2 - 5x + 6.

  • Setting it equal to zero, we get x^2 - 5x + 6 = 0.

  • Factoring the polynomial, we get (x - 2)(x - 3) = 0.

  • Therefore, the zeros of the polynomial are x = 2 and x = 3.



Relationship between Zeros and Coefficients:

  • The relationship between the zeros and the coefficients of a quadratic polynomial is given by Vieta's formulas.

  • For a quadratic polynomial ax^2 + bx + c, the sum of the zeros is -b/a and the product of the zeros is c/a.

  • In this case, the sum of the zeros is 5 and the product of the zeros is 6.

  • Verifying the relationship, we have -b/a = -(-5)/1 = 5 and c/a = 6/1 = 6.

  • Therefore, the relationship between the zeros and the coefficients is verified.

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Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficient x*2 -5x + 6?
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