Find the product of the roots 3(x+3)²+5(x+3)-2=0
Answers
Solution:-
Equation
=> 3(x + 3 )² + 5( x + 3 ) - 2 = 0
=> 3( x² + 3² + 2× x × 3 ) + 5x + 15 - 2 = 0
=> 3x² + 27 + 18 x + 5x + 15 - 2 = 0
=> 3x² + 23x + 40 = 0
Product of zero = c / a
equation is
=> 3x² + 23x + 40 = 0
a = 3 , b = 23 and c = 40
:- product of zero is c / a = 40/3
So answer is 40/3
About quadratic equation
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x). The values of x satisfying the quadratic equation are the roots of the quadratic equation (α,β).
The quadratic equation will always have two roots. The nature of roots may be either real or imaginary.
Answer:
40/3
Step-by-step explanation:
let a=x+3, then equation becomes
3a^2+5a-2=0
3a^2+6a-a-2=0
3a(a+2)-1(a+2)=0
(3a-1)(a+2)=0
replace a=x+3
(3(x+3)-1)(x+3+2)=0
(3x+8)(x+5)=0
x=-8/3, -5
product of roots =40/3
Alternatively
(3x+8)(x+5)=0
3x^2+23x+40=0
product of roots=c/a =40/3
hope this helps