Question

Find the quadratic polynomial whose zeros are 2 + 1 by root 2 and 2 minus one by root 2

Answer 1

Answer:

Root2xsquare - 3x + 1

Step-by-step explanation:

-b/a=2+1/root2

c/a=2-1/root2

Therefore a= root 2

b= -3

c=1

Therefore poly. = root2x^2 - 3x + 1

Answer 2

$2x^2 - 8x + 7 = 0$ is the quadratic polynomial whose zeros are 2 + 1 by root 2 and 2 minus one by root 2

Solution:

The general quadratic equation is given as:

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

From given,

zeros are:

$2 + \frac{1}{\sqrt{2} } \\\\2 - \frac{1}{\sqrt{2}}$

Find sum of zeros:

$Sum\ of\ zeros = 2 + \frac{1}{\sqrt{2}} + 2 - \frac{1}{\sqrt{2}} \\\\Sum\ of\ zeros = 4$

Find product of zeros:

$Product\ of\ zeros = (2 + \frac{1}{\sqrt{2} } ) \times ( 2 - \frac{1}{\sqrt{2}}) \\\\Product\ of\ zeros = 2 ^2 - (\frac{1}{\sqrt{2}})^2 \\\\Product\ of\ zeros = 4 - \frac{1}{2} \\\\Product\ of\ zeros = \frac{7}{2}$

Substituting we get,

$x^2 - 4x + \frac{7}{2} = 0 \\\\2x^2 - 8x + 7 = 0$

Thus the equation is found

Learn more:

Find the zeroes of the quadratic polynomial and verify the relationship between the zeros and the coefficient

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