Question

Form the equations whose roots are ±2 under root 3 - 5

Answer 1

Answer:

Quadratic Equation is

${x}^{2} + 10x + 13 = 0$

Step-by-step explanation:

Let the Roots of the quadratic equation be

$m = 2 \sqrt{3} - 5 \: and \: n = - 2 \sqrt{3 } - 5$

The sum of the roots is (m+n) and the product of the roots is (mn). And the quadratic equation is

${x}^{2} - (m + n)x + mn = 0$

$m + n = (2 \sqrt{3} - 5) + ( - 2 \sqrt{3} - 5) \\ = 2 \sqrt{3} - 5 - 2 \sqrt{3} - 5 \\ = - 10 \\ \\ mn = (2 \sqrt{3} - 5)( - 2 \sqrt{3} - 5) \\ = -4 \times 3 - 10 \sqrt{3} + 10 \sqrt{3} + 25 \\ = - 12 + 25 \\ = 13$

Insert the values of m+n and mn in the quadratic equation

${x}^{2} - (m + n)x + mn = 0 \\ {x}^{2} - ( - 10)x + 13 = 0 \\ {x}^{2} + 10x + 13 = 0$