Question

if alpha and beta are the zeros of the polynomial find this answer please

Answer 1

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Answer 2

2x² - 5x + k = 0

Sum of zeroes = ã ( alpha) + ß(beta) = - b / a
= 5 / 2

It is given that ã - ß = 5

So ã + ß = 5/2

2(ã + ß) = 5

2ã + 2ß = 5 ...(1)

and ã - ß = 5 ..(2)

Therefore ã = 5 + ß ...(3)

put the value of ã in equation in equation (1).

2 ( 5 + ß ) + 2ß = 5

10 + 2ß + 2ß = 5

4ß = 5 - 10

4ß = -5

ß = -5/4

put the value of ß in equation (3).

ã = 5 + (-5/4)

= 5 - 5/4

= 20 - 5 /4

= 15 /4

Now product of zeroes = ãß = c/a

k /2 = 15/4 × -5 /4

k / 2 = ( - 75 / 16)

k = (- 75 / 16) × 2

k = (- 75 / 8)

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