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