Question

please solve the question with explaination.

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Answer 1

Answer:

Hope this may help you.......

Answer 2

$\huge{\green{\boxed{\mathbb{\red{ANSWER}}}}}$

$a {x}^{2} + 15x + 6$

Let the zeros of the given polynomial be $\alpha \: and \frac{1}{ \alpha }$

Product of zeros = $\frac{c}{a} = \frac{6}{a}$

$=> \alpha \times \frac{1}{ \alpha } = \frac{6}{a} \\ => 1 = \frac{6}{a} => a = 6$

And Sum of zeros =

$\frac{ - b}{a} = \frac{ - 15}{6} = \frac{ - 5}{2}$

$=> \alpha + \frac{1}{ \alpha } = \frac{ - 5}{2}$

Squaring Both Sides

$=> {( \alpha + \frac{1}{ \alpha }) }^{2} = {( \frac{ - 5}{2}) }^{2} \\ => {( \alpha - \frac{1}{ \alpha } }^{2} - 4 = \frac{25}{4} \\ => \alpha - \frac{1}{ \alpha } = \sqrt{ \frac{25}{4} - 4 } \\ => \alpha - \frac{1}{ \alpha } = \sqrt{ \frac{9}{4} } \\ = > \alpha - \frac{1}{ \alpha } = \frac{3}{2}$

Hope this helps!!!!!!!