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

Question

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

Answer

Answer

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.

Answer

I think equation is x^2 - 5x + 6
Then see ---
x^2 - 5x + 6
Apply middle term split
x^2 - 3x -2x + 6 = 0
x ( x - 3 ) - 2 ( x - 3 ) = 0
( x - 2 ) ( x - 3 ) = 0
x = 2 or x = 3
Sum of zeroes = - b / a = - ( - 5 ) / 1 = 5
Product of zeroes = c / a = 6 / 1 = 6

Answer

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