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:-

${x}^{2} + 5x + a = 0\\ ax²+bx+c\\a=1, c= a \\ product \: of \: root = \frac{c}{ a} = 1 \\ product \: of \: root = \frac{a}{ 1 } = 1 \\ a = 1$

Second part :-

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

Values of a is :- 1 and 4