Question

write the quadratic equation of whose roots are 1/root 2, 1/root2​

Answer 1

Answer:

x² -x/√2+1/2= 0 is ur ans

Answer 2

The quadratic equation of whose roots are 1/root 2, 1/root 2​ are $2x^2 - 2\sqrt{2}x + 1 = 0$

Solution:

The quadratic equation is given as:

$x^2 - (\text{ sum of zeros })x + \text{ product of zeros } = 0$

From given,

Zeros = $\frac{1}{\sqrt{2}} , \frac{1}{\sqrt{2}}$

Thus,

$\text{sum of zeros } = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}$

$\text{sum of zeros } = \frac{2}{\sqrt{2}}$

$\text{product of zeros } = \frac{1}{\sqrt{2}} \times \frac{1}{\sqrt{2}}\\\\\text{product of zeros } = \frac{1}{2}$

Therefore,

$x^2 - \frac{2}{\sqrt{2}}x + \frac{1}{2} = 0\\\\x^2 - \sqrt{2}x + \frac{1}{2} = 0\\\\2x^2 - 2\sqrt{2}x + 1 = 0$

Thus the equation is found

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