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Question

If a and b are the roots of the equation $$\displaystyle x^{2}-1=0$$ the form of quadratic equation whose roots are 2a and 2b will be-


A
x242=0
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B
x2+4=0
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C
x24=0
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D
x2+42=0
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Solution

The correct option is C $$\displaystyle x^{2}-4=0$$
$$\Rightarrow$$  $$a$$ and $$b$$ are roots of the quadratic equation 

$$x^2-1=0$$
So, $$x^2-1=0$$
$$\Rightarrow$$  $$x^2=1$$

$$\therefore$$  $$x=\pm 1$$
Let $$a=+1$$ and $$b=-1$$

Then, $$2a=2$$ and $$2b=-2$$

The required quadratic equation,
$$(x-2a)(x-2b)=0$$
$$\Rightarrow$$  $$(x-2)(x+2)=0$$

$$\Rightarrow$$  $$x^2+2x-2x-4=0$$

$$\therefore$$  $$x^2-4=0$$

The required quadratic equation is $$x^2-4=0$$.

Mathematics

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