Find the solution to the equation below. 2x^2+3x-20=0
1 answer:
Answer:
x = -4, 5/2
Step-by-step explanation:
A quadratic can be solved may ways, including graphing, factoring, and the quadratic formula. You can also check possible answers by making use of the relationships between solutions and the coefficients.
__
A graph is attached. It shows the solutions to be -4 and 5/2.
__
When factored, the equation becomes ...
(2x -5)(x +4) = 0 . . . . . has solutions x=-4, x=5/2 (these make the factors zero)
__
Using the quadratic formula, the solutions of ax^2 +bx +c = 0 are found from ...
x = (-b±√(b²-4ac))/(2a)
x = (-3±√(3²-4(2)(-20))/(2(2)) = (-3±√169)/4 = {-16, +10}/4
x = {-4, 5/2}
__
For ax^2 +bx +c = 0, the solutions must satisfy ...
product of solutions is c/a = -20/2 = -10
Only the first and last choices have this product.
sum of solutions is -b/a = -3/2
Only the first choice (-4, 5/2) has this sum.
You might be interested in
You can use cross product to slove this equation.
