Question

Find a quadratic polynomial whose zeroes are 7+√5and7-√5

Answer 1

The required quadratic polynomial is  $x^2-14x+44$

Step-by-step explanation:

Given that for a quadratic polynomial whose zeroes are $7+\sqrt{5}$ and $7-\sqrt{5}$

To find the quadratic equation from the given zeros :

• First find the sum of the zeros
• $Sum of zeros=7+\sqrt{5}+7-\sqrt{5}$
• $=7+7$

Therefore the sum of the zeros=14

• Now $Product of zeros=(7+\sqrt{5})(7-\sqrt{5})$
• $=(7^2-(\sqrt{5})^2)$ ( by using the identity $(a+b)(a-b)=a^2-b^2$)
• $=49-5$
• $=44$
• Therefore the $Product of zeros=44$

For a quadratic equation we may write

$x^2-(sum of zeros)x+product of zeros$

• Now substitute the values we get
• $x^2-(14) x +44$
• $x^2-14x+44$

Hence the required quadratic polynomial is  $x^2-14x+44$