Question

Factorise
x²+2√3x - 24​

Answer 1

Answer:

=x²+2√3x-24

=x²+4√3x-2√3x-24

=x(x+4√3)-2√3(x+4√3)

=(x+4√3)(x-2√3)

Answer 2

Given :-

• x²+2√3x-24

To find :-

• Solve the expression ?

Solution:-

• Given polynomial is x²+2√3x-24

$\qquad$☀️ Here, 24 can be written as :-

$\qquad\leadsto\quad \pmb {\mathfrak{24 = 2×2×2×3}}$

$\qquad\leadsto\quad \pmb {\mathfrak{24 = 2×2×2×√3×√3}}$

$\blue{\qquad\leadsto\quad \pmb {\mathfrak{24 = 4√3×2√3}}}$

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$\pink{\qquad\leadsto\quad \pmb {\mathfrak{x²+2√3x-24}}}$

$\qquad\leadsto\quad \pmb {\mathfrak{x²+2√3x-(4√3×2√3)}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ x²+4√3x-2√3x-(4√3×2√3)}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ x(x+4√3) -2√3(x+4√3)}}$

$\blue{\qquad\leadsto\quad \pmb {\mathfrak{ (x+4√3)(x-2√3)}}}$

$\qquad\small\underline{\pmb{\sf \:According \: to \: the \: question :-}}$

$\qquad$☀️ To get zeroes we write the polynomial is equal to zero.

$\qquad\leadsto\quad \pmb {\mathfrak{(x+4√3)(x-2√3)=0}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ x+4√3 = 0 \;or \;x-2√3 = 0}}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ x = -4√3 \;or \;x = 2√3}}}$

• Zeroes of the given polynomial are -4√3 and 2√3.

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