Question

find the quadratic polynomial whose zeroes are 4+root 5 and 4-root 5​

Answer 1

Answer:

the quadratic equation will be - x² -(4+√5+4-√5)x+(4+√5)(4-√5)

Step-by-step explanation:

si answer is =x² - 8x+11

Answer 2

The quadratic polynomial whose zeroes are 4 + root 5 and 4 - root 5​ is $x^2 - 8x + 11 = 0$

Solution:

Given that,

Quadratic polynomial has zeros:

$4 + \sqrt{5} \text{ and } 4 - \sqrt{5}$

The general quadratic equation is given as:

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

Find sum of zeros:

$\text{ sum of zeros } = 4 + \sqrt{5} + 4 - \sqrt{5}\\\\\text{ sum of zeros } = 8$

Find product of zeros:

$\text{product of zeros } = 4 + \sqrt{5} \times 4 - \sqrt{5} \\\\\text{product of zeros } = 4^2 - (\sqrt{5})^2\\\\\text{product of zeros } = 16 - 5\\\\\text{product of zeros } = 11$

Thus the quadratic polynomial is:

$x^2 - 8x + 11 = 0$

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