Find the Zeros of the Quadratic Polynomial 4u²+8u and Verify the Relationship between the Zeros and the Coefficient

Solution

To find the zeros of the quadratic polynomial 4u²+8u, we can factor out the greatest common factor of 4u, which gives:

4u(u + 2) = 0

To find the zeros, we set each factor equal to zero and solve for u:

4u = 0 or u + 2 = 0

u = 0 or u = -2

So the zeros of the quadratic polynomial 4u²+8u are u = 0 and u = -2.

Now, let's verify the relationship between the zeros and the coefficient of the quadratic polynomial. The coefficient of the quadratic term (u²) is 4, and the constant term is 0. The sum of the zeros is:

0 + (-2) = -2

And the product of the zeros is:

0 × (-2) = 0

We can see that the sum of the zeros, -2, is equal to -b/a, where b is the coefficient of the linear term (8) and a is the coefficient of the quadratic term (4). And the product of the zeros, 0, is equal to c/a, where c is the constant term (0) and a is the coefficient of the quadratic term (4). This verifies the relationship between the zeros and the coefficients of the quadratic polynomial:

• sum of zeros = -b/a = -(8/4) = -2
• product of zeros = c/a = 0/4 = 0

Answer

Zeros of the quadratic polynomial 4u²+8u are u = 0 and u = -2.

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