Find the Quadratic Polynomial, Sum of Whose Zeros is (5/2) and Their Product is 1. Hence, Find the Zeros of the Polynomial
To find the quadratic polynomial with a sum of zeros equal to 5/2 and a product of zeros equal to 1, let's denote the zeros as p and q.
- Sum of zeros: p + q = 5/2
- Product of zeros: pq = 1
Using these conditions, we can construct the quadratic polynomial:
x2 - (p + q)x + pq = 0
Substituting the given values:
x2 - (5/2)x + 1 = 0
The quadratic polynomial is 2x2 - (5)x + 2 = 0.
To find the roots of the quadratic equation 2x2 - 5x + 2 = 0, we can use the quadratic formula:
x = (-b ± √(b2 - 4ac)) / (2a)
In this case, a = 2, b = -5, and c = 2. Substituting these values into the quadratic formula:
x = (5 ± √((-5)2 - 4(2)(2))) / (2(2)) = (5 ± √(25 - 16)) / 4 = (5 ± √9) / 4 = (5 ± 3) / 4
So the roots of the quadratic equation 2x2 - 5x + 2 = 0 are: x = (5 + 3) / 4 = 8 / 4 = 2 x = (5 - 3) / 4 = 2 / 4 = 1/2
Therefore, the roots of the quadratic equation are x = 2 and x = 1/2.
The Quadratic Polynomial is 2x2 - (5)x + 2 = 0, Sum of Whose Zeros is (5/2) and Their Product is 1. Hence, the Zeros of the Polynomial are x = 2 and x = 1/2
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