Question
Short-Answer Question:
Write the zeros of the quadratic polynomial $\text{f}(\text{x})=4\sqrt3\text{x}^2+\text{5x}-2\sqrt3$
Write the zeros of the quadratic polynomial $\text{f}(\text{x})=4\sqrt3\text{x}^2+\text{5x}-2\sqrt3$
✓
Answer
We have,
$\text{f}(\text{x})=4\sqrt3\text{x}^2+\text{5x}-2\sqrt3$
$=4\sqrt3\text{x}^2+\text{8x}-\text{3x}-2\sqrt3$
$=\text{4x}\big(\sqrt3\text{x}+2\big)-\sqrt3\big(\sqrt3\text{x}+2\big)$
$=\big(\text{4x}-\sqrt3\big)\big(\sqrt3\text{x}+2\big)$
$\therefore\text{f}(\text{x})=0$
$\Rightarrow\big(\text{4x}-\sqrt3\big)\big(\sqrt3\text{x}+2\big)=0$
$\Rightarrow\text{4x}-\sqrt3=0$ or $\sqrt3\text{x}+2$
$\Rightarrow\text{x}=\frac{\sqrt3}{4}$ or $\text{x}=-\frac{2}{\sqrt3}$
So, the zeros of f(x) are $\frac{\sqrt3}{4}$ and $-\frac{2}{\sqrt3}$
$\text{f}(\text{x})=4\sqrt3\text{x}^2+\text{5x}-2\sqrt3$
$=4\sqrt3\text{x}^2+\text{8x}-\text{3x}-2\sqrt3$
$=\text{4x}\big(\sqrt3\text{x}+2\big)-\sqrt3\big(\sqrt3\text{x}+2\big)$
$=\big(\text{4x}-\sqrt3\big)\big(\sqrt3\text{x}+2\big)$
$\therefore\text{f}(\text{x})=0$
$\Rightarrow\big(\text{4x}-\sqrt3\big)\big(\sqrt3\text{x}+2\big)=0$
$\Rightarrow\text{4x}-\sqrt3=0$ or $\sqrt3\text{x}+2$
$\Rightarrow\text{x}=\frac{\sqrt3}{4}$ or $\text{x}=-\frac{2}{\sqrt3}$
So, the zeros of f(x) are $\frac{\sqrt3}{4}$ and $-\frac{2}{\sqrt3}$
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