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The quadratic below 2x^(2)+14x=-24

User Hewa Jalal
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Firstly, we need to rearrange the equation 2x^2 + 14x + 24 = 0 to its standard form, which is already given.

To find the roots of this quadratic equation, we utilize the Quadratic Formula:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

Our coefficients for the quadratic equation are a = 2, b = 14, and c = 24.

Before we can find the roots, we need to check the discriminant (b^2 - 4ac). The discriminant will help us to know the number of roots in the given quadratic equation.

So our discriminant will be:
(14^2) - (4*2*24) = 196 - 192 = 4

Since the discriminant is greater than zero, it means that we are dealing with two distinct roots.

Now let's substitute a, b, and c into the quadratic formula to find our roots.

For the root1 which is x:

x = [-14 + sqrt(4)] / 2*2
x = [-14 + 2] / 4
x = -12 / 4
x = -3.0

For the root2 which is y:

y = [-14 - sqrt(4)] / 2*2
y = [-14 - 2] / 4
y = -16 / 4
y = -4.0

So, the solutions to the quadratic equation 2x^2 + 14x + 24 = 0 are x=-3 and y=-4.

User Jiew Meng
by
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