Question

Obtain the zeroes of quadratic polynomial
$\sqrt{3} \: x {}^{2} - \: 8x \: + \: 4 \sqrt{3}$
and verify relationship between zeroes and co efficient

Answer 1

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We have

=> √3x² - 8x + 4√3 = 0

Here

=> a x c = √3 x 4√3

=> ac = 12

Thus we know 12 = 6 x 2

Thus by middle term splitting method

=> √3x² - 6x - 2x + 4√3 = 0

=> √3x(x - 2√3) - 2(x - 2√3) = 0

=> (√3x - 2)(x - 2√3) = 0

=> x = 2/√3 or x = 2√3 <<<<<< Answer

Verifying relation between zeros and their co efficients

Let alpha = 2/√3 and beta = 2√3

Then alpha + beta = - b/a

=> 2√3 + 2/√3 = 8/√3

=> (6 + 2)/√3 = 8/√3

=> 8/√3 = 8/√3

Verified

Similarly

alpha (beta) = c/a

=> 2/√3 (2√3) = 4

Cutting √3

=> 4 = 4

Hence Verified


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