Question

write the quadratic equation whose zeores are
5- 2✓3 and 5 + 2 ✓3
​

Answer 1

Answer:

alpha +beta =5-2√3+5+2√3=10

alpha *beta =5-2√3*5+2√3=(5)^2-(2√3)^2=(25-4*3)=25-12=13

therefore the quadratic equation is

=X^2-(alpha+beta)x+ (alpha*beta)

=x^2-10x+13

Answer 2

Answer:

$let \: given \: zeros \: are \: \alpha \: and \: \beta \: so \: \alpha + \beta = 5 - 2 \sqrt{3} + 5 + 2 \sqrt{3} = 10 \: and \: \alpha \times \beta = 25 - 12 = 13 \: so \: equation \: is \: {x}^{2} - ( \alpha + \beta )x \: + \alpha \beta = 0 \: ie \: \: {x}^{2} - 10x + 13 = 0.$