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Find zeroes of the polynormial 6x^(2)-3-...

Find zeroes of the polynormial `6x^(2)-3-7x`

A

`x = 5/2 or x = 1/3.`

B

`x = 3/2 or x = 5/3.`

C

`x = 3/2 or x = 7/3.`

D

`x = 3/2 or x = -1/3`

Text Solution

Verified by Experts

The correct Answer is:
D
Let the given polynomial by f(x). Then,
` f(x) = 6x^(2)-3 - 7x`
`= 6x^(2) = 7x - 3` [in standard form]
` = 6x^(2) - 9x + 2x - 3`
` = 3x(2x-3)+(2x-3)`
` = (2x-3)(3x+1).`
`:. F(x) = 0 rArr (2x-3) (3x+1) = 0`
` rArr 2x - 3 = 0 or 3x + 1 = 0 `
` rArr x = 3/2 or x = 1/3.`
So, the zeros of f(x) are `3/2 and (-1)/3.`
Sum of zeros = `{3/2+((-1)/3)}= (3/2-1/3) = 7/6 = (-"(coefficient of x )")/(("coefficient of" x^(2))).`
Procuct of zeros = `3/2 xx ((-1)/3) = (-3)/6 = ("constant term")/("coefficient of " x^(2)) .`
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