Find a Quadratic Polynomial Whose Sum and Product of Zeros Are 21/8 and 5/16 and Find Its Zeros by Factorisation

Video Explanation

Watch the video explanation below:

Solution

Given:

Sum of zeros = 21/8
Product of zeros = 5/16

Step 1: Form the Quadratic Polynomial

If sum of zeros = α + β and product of zeros = αβ, then the quadratic polynomial is:

x² − (α + β)x + αβ

∴ Required polynomial:

x² − (21/8)x + 5/16

Multiplying throughout by 16 to remove fractions:

16x² − 42x + 5

Step 2: Find the Zeros by Factorisation

16x² − 42x + 5 = 0

Split the middle term:

16x² − 40x − 2x + 5 = 0

Grouping the terms:

8x(2x − 5) − 1(2x − 5) = 0

(8x − 1)(2x − 5) = 0

∴ 8x − 1 = 0   or   2x − 5 = 0

∴ x = 1/8   or   x = 5/2

Zeros of the polynomial are 1/8 and 5/2.

Step 3: Verification

Let α = 1/8 and β = 5/2

Sum of zeros:

α + β = 1/8 + 5/2 = 21/8

✔ Verified

Product of zeros:

αβ = (1/8)(5/2) = 5/16

✔ Verified

Final Answer

Required quadratic polynomial is 16x² − 42x + 5.

Zeros of the polynomial are 1/8 and 5/2.

Conclusion

Thus, the quadratic polynomial formed using the given sum and product of zeros satisfies all the required conditions, and its zeros are obtained correctly by the factorisation method.