Question

if zeroes of the polynomial x^2 + 4x+2a are alpha and 2/alpha,find the value of a​

Answer 1

${\huge{\star}{\color{skyblue}{\rm{Answer}}}} \huge\star$

Zeroes are:-

$\sf \alpha \: and \: \frac{2}{ \alpha} \\ \\ \sf \: sum \: of \: zeroes = (\alpha + \frac{2}{ \alpha} ) = \frac{ - b}{a} \\ \\ \sf product \: of \: zeroes = (\alpha \times \ \frac{2}{ \alpha} ) = \frac{c}{a}$

It is clear from given equation that value of:-

• a=1 which is coefficient of x².
• b=4 which is coefficient of x.
• c=2a which is constant term.

$\sf So \: product \: of \: zeroes = 2a$

Product of zeroes:-

$\sf \frac{2}{ \cancel \alpha} \times \cancel\alpha = 2a$

2=2a

$\large \boxed{ \sf \red {1 = a}}$

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