Find the Quadratic Polynomial, Sum of Whose Zeros is (5/2) and Their Product is 1. Hence, Find the Zeros of the Polynomial

By Mohit Uniyal|Updated : May 24th, 2023

Find the quadratic polynomial, sum of whose zeros is (5/2) and their product is 1. Hence, find the zeros of the polynomial.

Here are the steps which we will be using to find the quadratic polynomial and zeros of the polynomial.

  • Step 1: Let's denote the zeros as p and q.
  • Step 2: We know that the sum of zeros is given by p + q = 5/2, and the product of zeros is given by pq = 1.
  • Step 3: Construct the quadratic polynomial using the zeros: The quadratic polynomial is given by (x - p)(x - q) = 0.
  • Step 4: Expand the equation:
  • Step 5: Find the zeros of the polynomial using quadratic formula

Find the Quadratic Polynomial, Sum of Whose Zeros is (5/2) and Their Product is 1. Hence, Find the Zeros of the Polynomial

Solution:

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.

Given information:

  • 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.

Answer:

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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