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Ray Of Light [21]
3 years ago
12

Find the solution to the equation below. 2x^2+3x-20=0

Mathematics
1 answer:
mariarad [96]3 years ago
8 0

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.

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