Answer to Question #228324 in Algebra for Leu

Question

. If one root of the quadratic equation ૛࢞૞ − ૛࢞ + ࢑ ૙ = is the reciprocal of the other

then find ࢑ .

Answer 1

$$ax^2+bx+c=0, a\not=0$$

Given that one root of the quadratic equation is the reciprocal of the other

$$x_1x_2=1$$

Then

$$D=b^2-4ac\geq0$$

$$x_1x_1=\dfrac{c}{a}=1=>c=a$$

$$b^2-4a^2\geq0$$

$$|b|\geq2|a|$$

$a\not=0, |b|\geq2|a|, c=a.$