Question

Find all values of a for which

(x² + 5x + a)(4x² - 7x+a)=0
The products of all roots of the equation is equal to 1

Answer 1

Question:- Find the Value of a

Equation:-

`({x}^(2) + 5x + a)(4 {x}^(2) - 7x + a) = 0 \\`

Given :- product of roots = 1

Answer :- 4 and 1

Explanation:-

`({x}^(2) + 5x + a)(4 {x}^(2) - 7x + a) = 0 \\`

First part:-

`{x}^(2) + 5x + a = 0\\ ax²+bx+c\\a=1, c= a \\ product \: of \: root = (c)/( a) = 1 \\ product \: of \: root = (a)/( 1 ) = 1 \\ a = 1\\`

Second part :-

`(4 {x}^(2) - 7x + a) = 0\\ ax²+bx+c\\ a= 4 , c= a \\ product \: of \: root = (c)/( a) = 1 \\ product \: of \: root = (a)/( 4) = 1 \\ a = 4`

Values of a is :- 1 and 4