What are the solutions of the quadratic equation?
4x2 + 34x + 60 = 0
(1 point)
Responses
6, two-thirds
6, Image with alt text: two-thirds
–5 over 2, –two-thirds
– Image with alt text: 5 over 2 , – Image with alt text: two-thirds
–6, – 5 over 2
–6, – Image with alt text: 5 over 2
–6, 4
The solutions of the quadratic equation 4x^2 + 34x + 60 = 0 are:
-6, -5/2
To find the solutions of the quadratic equation 4x^2 + 34x + 60 = 0, we can use the quadratic formula. The quadratic formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, we have a = 4, b = 34, and c = 60. Substituting these values into the quadratic formula, we get:
x = (-(34) ± √((34)^2 - 4(4)(60))) / (2(4))
Simplifying further:
x = (-34 ± √(1156 - 960)) / 8
x = (-34 ± √196) / 8
x = (-34 ± 14) / 8
This gives us two possible solutions:
x1 = (-34 + 14) / 8 = -20 / 8 = -5 / 2
x2 = (-34 - 14) / 8 = -48 / 8 = -6
Therefore, the solutions of the quadratic equation 4x^2 + 34x + 60 = 0 are:
x = -5/2 or x = -6.
To find the solutions of a quadratic equation, we can use the quadratic formula. The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the given equation, 4x^2 + 34x + 60 = 0, we can identify that a = 4, b = 34, and c = 60.
Now, substituting the values into the quadratic formula, we get:
x = (-(34) ± √((34)^2 - 4(4)(60))) / (2(4))
Simplifying further:
x = (-34 ± √(1156 - 960)) / 8
x = (-34 ± √196) / 8
The square root of 196 is 14, so we have:
x = (-34 ± 14) / 8
This can be further simplified as:
x1 = (-34 + 14) / 8 = -20 / 8 = -5/2
x2 = (-34 - 14) / 8 = -48 / 8 = -6
Therefore, the solutions of the quadratic equation 4x^2 + 34x + 60 = 0 are -5/2 and -6.