Question

Find the zeros of the quadratic polynomial 4root3X^3 +5X -2root3 and verify the relation between the
zeros and its coefficients,
L

Answer 1

Answer:

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Answer 2

☆ ANSWER

● Given polynomial:-

$4 \sqrt{3}x {}^{2} + 5x - 2 \sqrt{3}$

● To find:-

Zeroes of the given polynomial.

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● Now,

4 \sqrt{3}x {}^{2} + 5x - 2 \sqrt{3}

= 4 \sqrt{3}x {}^{2} + (8-3)x - 2 \sqrt{3}

{By middle term splitting

{By middle term splittingi.e. 4 \sqrt{3}×2 \sqrt{3} = 24 And 24 = 2×2×2×3 Also 2×2×2-3 = 5}

= 4 \sqrt{3}x {}^{2} + 8x - 3x - 2 \sqrt{3}

= 4x( \sqrt{3}x + 2) - \sqrt{3}( \sqrt{ 3} x + 2)

$= (x - \sqrt{3})( \sqrt{3}x + 2)$

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● So if the above terms are zeros of thebgiven polynomial then Either,

=》 (x - \sqrt{3}) = 0 or ( \sqrt{3}x + 2) = 0

=》 x = sqrt{3} or x = -2/sqrt{3}.

● Therefore the required roots of the polynomial are sqrt{3} and -2/sqrt{3}.

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