Question

the sum of the reciprocal of the polynomial 2x^2-5x+8

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Answer 1

Answer:

1/+2x^2-5x+8

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Answer 2

Answer:

5/8

Note:

If A and B are the zeros of the quadratic polynomial ax² + bx + c , Then ;

Sum of zeros , (A+B) = -b/a

Product of zeros (A•B) = c/a

Solution:

Here,

The given quadratic polynomial is;

2x² - 5x + 8 .

Clearly,

a = 2

b = -5

c = 8

Let A and B are the zeros of the given quadratic polynomial.

Then,

Sum of zeros = -b/a

=> A + B = -(-5)/2 = 5/2

Also,

Product of zeros = c/a

=> A•B = 8/2 = 4

Now,

We need to find the sum of zeros of the given quadratic polynomial.

Thus,

1/A + 1/B = (B + A) / A•B

= (A + B) / A•B

= (5/2) / 4

= 5/2•4

= 5/8

Hence,

The required answer is 5/8 .