Question

given that α and β are the roots of the equation 2x^2-3x+4 = 0,find an equation whose roots are...

Answer 1

\[\alpha+\frac{ 1 }{\alpha} and \beta+\frac{ 1 }{\beta}\]

Answer 2

there must be a better way and easier....

Answer 3

we know ab=2

Answer 4

\(\alpha + \beta = 3/2 \text{ and } \alpha \beta = 2\)
Sum of roots of the new equation is:
\(\large \alpha + \beta + \frac{\alpha+\beta}{\alpha \beta} = \frac{3}{2} +\frac{3/2}{2} = \frac{9}{4}\)

Product of roots of the new equation is:
\(\large (\alpha + \frac{1}{\alpha })(\beta + \frac{1}{\beta}) = \alpha \beta + \frac{\alpha ^{2}+ \beta^{2}}{\alpha \beta} + \frac{1}{\alpha \beta}\)

Now, \(\alpha^{2} + \beta^{2} = (\alpha+\beta)^{2} - 2\alpha \beta\)

Substitute the values in the above expression.
If the sum of roots is \(s\) and the product of roots is \(p\) ofa quadratic equation,
then the equation is given by:
\(x^{2}-sx + p=0\)

Answer 5

a+b=3/2

Answer 6

yes, thats easier way....