Question

x2+3sqrt3x+6 factorize it by splitting the middle term

Answer 1

Question:-

→Factorize by splitting the middle term↓

•i)x²+3√3x+6

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AnsWer:-

→x²+3√3+6=0

๛S=3√3[Sum of Equation]

๛P=6[Product of Equation]

•2√3×√3=2×3=6→P

•2√3+√3=3√3→S

→x²+2√3x+√3x+6=0

→x(x+2√3)+√3(x+2√3)=0

→x+√3=0

→x+2√3=0

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•Taking x+√3

→x+√3=0

→x=-√3

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•Taking x+2√3

→x+2√3=0

→x=-2√3

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★Hence The zeros are [-√3]&[-2√3]★

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Answer 2

$\huge{\underline{\underline{\red{Answer→}}}}$

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${x}^{2} + 3 \sqrt{3} x + 6 \\ = {x}^{2} + 2 \sqrt{3} x + \sqrt{3} x + 6 \\ = x(x + 2 \sqrt{3} ) + \sqrt{3} (x + 2 \sqrt{3} ) \\ = (x + \sqrt{3})(x + 2 \sqrt{3} )$

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The roots of this Polynomial →

First Root ↓

$x + \sqrt{3} = 0 \\ x = - \sqrt{3}$

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Second Root ↓

$x + 2 \sqrt{3} = 0 \\ x = - 2 \sqrt{3}$

(-√3) and (-2√3) are the roots of this Polynomial.

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