Question

find the zeros of the following polynomials by factorization method and verify the relation between the zeros and the coefficients of the polynomials 2x2+7/2x+3/4

Answer 1

hope this answer will be helpful

Answer 2

Finding the zeroes:

The given polynomial is

f (x) = 2x² + 7/2 * x + 3/4

= (8x² + 14x + 3)/4

= (8x² + 14x + 3)/4

= {8x² + (12 + 2) x + 3}/4

= {8x² + 12x + 2x + 3}/4

= {4x (2x + 3) + 1 (2x + 3)}/4

= 1/4 * (2x + 3) (4x + 1)

So we can conclude that the zeroes are - 3/2 and - 1/4.

Verification:

The polynomial is f (x) = 2x² + 7/2 * x + 3/4

If p and q be the zeroes, we write:

• p + q = - (7/2)/2 = - 7/4
• pq = (3/4)/2 = 3/8

We have found the zeroes already:

• sum = - 3/2 - 1/4 = - 7/4
• product = (- 3/2) * (- 1/4) = 3/8

Thus verified.

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