Let f(y)=6y²-7y+2

6y²-3y-4y+2=0

3y(2y-1)-2(2y-1)=0

3y-2=0 2y-1=0

3y=2. 2y=1

y=2/3 y=1/2

Relation between roots

sum of the roots=-b/a=7/6

product of the roots=c/a=1/3

Introduction:
In mathematics, a quadratic polynomial is an expression of the form ax^2 + bx + c, where a, b, and c are constants and x is a variable. The quadratic polynomial is also known as a quadratic equation. In this question, we need to find the zeros of the quadratic polynomial and verify the relationship between the zeros and the coefficient.

Finding the zeros:
To find the zeros of a quadratic polynomial, we need to solve the equation ax^2 + bx + c = 0. In our case, the quadratic polynomial is 6y^2 - 7y + 2. So, we need to solve the equation 6y^2 - 7y + 2 = 0. We can solve this equation by using the quadratic formula, which is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

Here, a = 6, b = -7, and c = 2. Substituting these values into the formula, we get:

y = (-(-7) ± √((-7)^2 - 4(6)(2))) / 2(6)
y = (7 ± √13) / 12

Therefore, the zeros of the quadratic polynomial 6y^2 - 7y + 2 are (7 + √13) / 12 and (7 - √13) / 12.

Verifying the relationship between the zeros and the coefficient:
The relationship between the zeros of a quadratic polynomial and its coefficients is given by:

sum of zeros = -b/a
product of zeros = c/a

Here, a = 6, b = -7, and c = 2. Substituting these values into the formulas, we get:

sum of zeros = (-7/6) = -1.1667
product of zeros = (2/6) = 0.3333

We can verify that the sum of the zeros is equal to the negative of the coefficient of the linear term and the product of the zeros is equal to the constant term divided by the coefficient of the quadratic term. Therefore, the relationship between the zeros and the coefficient is verified.

Conclusion:
In this question, we found the zeros of the quadratic polynomial 6y^2 - 7y + 2 and verified the relationship between the zeros and the coefficient. The sum of the zeros is equal to the negative of the coefficient of the linear term and the product of the zeros is equal to the constant term divided by the coefficient of the quadratic term.