Question

4) Form a quadratic equation if the roots of the quadratic equation are 2+√7and 2-√7​

Answer 1

Given roots: 2+√7

2-√7

Sum = 2+√7 + 2-√7

= 4

Product = (2+√7)(2-√7)

$= {2}^{2} - ({ \sqrt{7} })^{2}$

$= 4 - 7$

$= - 3$

Now to form a quadratic equation,

${x}^{2} - (sum)x + (product)$

${x}^{2} - 4x - 3$

Answer 2

Answer:

Given roots: 2+√7

2-√7

Sum = 2+√7 + 2-√7

= 4

Product = (2+√7)(2-√7)

= {2}^{2} - ({ \sqrt{7} })^{2}=22−(7)2

= 4 - 7=4−7

= - 3=−3

Now to form a quadratic equation,

{x}^{2} - (sum)x + (product)x2−(sum)x+(product)

{x}^{2} - 4x - 3x2−4x−3