To solve the quadratic equation 3x^2 - 4x - 4 = 0 using the quadratic formula, we first need to identify the coefficients a, b, and c in the general quadratic equation form ax^2 + bx + c = 0.
In this case:
a = 3
b = -4
c = -4
Now, we can use the quadratic formula, which is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
Substitute the values of a, b, and c into the formula:
x = (4 ± √((-4)^2 - 4 * 3 * (-4))) / 2 * 3
x = (4 ± √(16 + 48)) / 6
x = (4 ± √64) / 6
Now, calculate the two possible values of x:
1. x = (4 + √64) / 6
x = (4 + 8) / 6
x = 12 / 6
x = 2
2. x = (4 - √64) / 6
x = (4 - 8) / 6
x = -4 / 6
x = -2/3
So, the two solutions to the quadratic equation 3x^2 - 4x - 4 = 0, correct to two decimal places, are:
Answers & Comments
Step-by-step explanation:
To solve the quadratic equation 3x^2 - 4x - 4 = 0 using the quadratic formula, we first need to identify the coefficients a, b, and c in the general quadratic equation form ax^2 + bx + c = 0.
In this case:
a = 3
b = -4
c = -4
Now, we can use the quadratic formula, which is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
Substitute the values of a, b, and c into the formula:
x = (4 ± √((-4)^2 - 4 * 3 * (-4))) / 2 * 3
x = (4 ± √(16 + 48)) / 6
x = (4 ± √64) / 6
Now, calculate the two possible values of x:
1. x = (4 + √64) / 6
x = (4 + 8) / 6
x = 12 / 6
x = 2
2. x = (4 - √64) / 6
x = (4 - 8) / 6
x = -4 / 6
x = -2/3
So, the two solutions to the quadratic equation 3x^2 - 4x - 4 = 0, correct to two decimal places, are:
x = 2 and x = -0.67 (approximately).
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Answer:
Solution
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Correct option is D)
3x
2
−4
3
x+4=0
a=3,b=−4
3
,c=4
Discriminant D=b
2
−4ac
=(−4
3
)
2
−4(3)(4)=48−48=0
⇒D=0
⇒ Two roots are equal.
The roots are
=
2a
−b±
D
=
2×3
4
3
±0
=
3
2
,
3
2
Hence, the roots are
3
2
and
3
2
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