Question

if α and β be the zeroes of the polynomial ax² + bx + c, then the value of √α / √β + √β / √α is
(1) b
(2) -b/√a√c
(3) -b/ac
(4) 1/ac

Answer 1

Answer:

$- b \div \sqrt{a} \sqrt{c}$

Step-by-step explanation:

For step by step explaination refer to the attachment............

Answer 2

Answer:

correct option is 3rd

Explanation:-)

As α and β are the roots of equation ax^2+bx+c.

So

α+β(sum of roots)= -b/a

and

αβ(product of roots)

=c/a

Now using these we can find the value of given question as follow :-

$\frac{ \sqrt{ \alpha } }{ \sqrt{ \beta } } + \frac{ \sqrt{ \beta } }{ \sqrt{ \alpha } } \\ = \frac{ \sqrt{ \alpha{}^{2} }+ \sqrt{ { \beta }^{2} } }{ \sqrt \alpha { \sqrt{ \beta } } } \\ = \frac{\alpha + \beta }{ \sqrt{ \alpha \beta } } \\As \: we \: have \: values \: of \: \alpha + \beta \\ and \: \\ \alpha \beta \\ so$

$= \frac{\frac{ - b}{a} }{ \sqrt{\frac{c}{a}} } \\ = \frac{ - b}{a} \times \sqrt{ \frac{a}{c} } \\ = \frac{ - b}{ \sqrt {ac} } \\ = \frac{ - b}{ \sqrt{a} \sqrt{c} }$