Question

if one zero of the polynomial (a^2+25)x^2+36x+10a is the reciprocal of the other, find the value of a?

Answer 1

Let the Zeros be b and 1 / b

( it is given in the question that Zeros is reciprocal )

Product of Zero =

$\frac{constant \: term}{coefficient \: of \: {x}^{2} }$

$b \times \frac{1}{b} = \frac{10a}{ {a}^{2} + 25}$

a² + 25 = 10a

a² - 10a + 25 = 0

a² - 5a - 5a + 25 = 0

a ( a - 5 ) - 5 ( a - 5 ) = 0

( a - 5 ) ( a - 5 ) = 0



( a - 5 ) = 0
a = 5

( a - 5 ) = 0
a = 5



Value of a = 5