Write the zeros of the quadratic polynomial fx - 4 -3 x2-5x-2-3-

F(x)=4√(3) x^2 +5x 2√(3) =0 ⇒ 4√(3) x^2 +8x 3x 2√(3)=0 ⇒ 4x(√(3) x+2) √(3)(√(3)x +2) =0 ⇒ (√(3)x +2)(4x √(3)) =0 ⇒ (√(3)x +2) =0 or (4x √(3)) =0 ⇒ x = ...

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Standard X

Mathematics

Solving a Quadratic Equation by Factorization Method

Write the zer...

Question

Write the zeros of the quadratic polynomial $f (x) = 4 \sqrt{3} x^{2} + 5 x - 2 \sqrt{3}$ .

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Solution

$f (x) = 4 \sqrt{3} x^{2} + 5 x - 2 \sqrt{3} = 0$

$\Rightarrow 4 \sqrt{3} x^{2} + 8 x - 3 x - 2 \sqrt{3} = 0$

$\Rightarrow 4 x (\sqrt{3} x + 2) - \sqrt{3} (\sqrt{3} x + 2) = 0$

$\Rightarrow (\sqrt{3} x + 2) (4 x - \sqrt{3}) = 0$

$\Rightarrow (\sqrt{3} x + 2) = 0 o r (4 x - \sqrt{3}) = 0$

$\Rightarrow x = \frac{- 2}{\sqrt{3}} o r \frac{\sqrt{3}}{4}$

So $\frac{- 2}{\sqrt{3}}$ and $\frac{\sqrt{3}}{4}$ are zeros of the given polynomial

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Write the zeros of the quadratic polynomial f(x)=4√3x2+5x−2√3.

f(x)=4√3x2+5x−2√3=0 ⇒4√3x2+8x−3x−2√3=0 ⇒4x(√3x+2)−√3(√3x+2)=0 ⇒(√3x+2)(4x−√3)=0 ⇒(√3x+2)=0 or (4x−√3)=0 ⇒x=−2√3 or √34 So −2√3 and √34 are zeros of the given polynomial

Write the zeros of the quadratic polynomial $f (x) = 4 \sqrt{3} x^{2} + 5 x - 2 \sqrt{3}$ .