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+1 vote
33.5k views
in Polynomials by (55.4k points)
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Find the zeroes of the quadratic polynomial √3x2 – 8x + 4√3 .

2 Answers

+2 votes
by (50.2k points)
selected by
 
Best answer

Let f(x) = √3 x2 – 8x + 4√3

By splitting the middle term, we get

f(x) = √3 x2 – 6x – 2x + 4√3

= √3 x(x – 2√3) – 2(x – 2√3)

= (√3 x – 2) (x – 2√3)

On putting f (x) = 0, we get

(√3 x – 2) (x – 2√3) = 0

⇒ √3 x – 2 = 0 or x – 2√(3 = 0)

x = 2/√3 or x = 2√3

Thus, the zeroes of the given polynomialimage√3 x2 – 8x + 4√3 are 2/√3 and 2√3

Verification

So, the relationship between the zeroes and the coefficients is verified.

+1 vote
by (17.0k points)

Given quadratic equation is √3x2 - 8x + 4√3 = 0

We should factorize the equation first.

By splitting the middle term, we get

= √3x2 - 6x - 2x + 4√3 = 0

= √3x(x - 2√3) - 2(x - 2√3) = 0

= (√3x - 2) (x - 2√3) = 0

= (√3x - 2) = 0, (x - 2√3) = 0

⇒ x = 2/√3, x = 2√3.

Thus, the zeros of the given polynomial √3x2 - 8x + 4√3 are 2/√3 and 2√3.

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