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x² + 29x + 208 = 0
y² + 19y + 78 = 0
- a)X > Y
- b)X < Y
- c)X ≥ Y
- d)X ≤ Y
- e)X = Y or relation cannot be established
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
x² + 29x + 208 = 0y² + 19y + 78 = 0a)X > Yb)X < Yc)X &...
Understanding the Quadratic Equations
To compare the values of X and Y from the given quadratic equations, we first need to find their roots.
Equation for X
For the equation:
x² + 29x + 208 = 0
Using the quadratic formula:
x = [-b ± √(b² - 4ac)] / 2a, where a = 1, b = 29, and c = 208.
Calculating the discriminant:
b² - 4ac = 29² - 4(1)(208) = 841 - 832 = 9.
Now, substituting back into the formula:
x = [-29 ± √9] / 2 = [-29 ± 3] / 2.
Calculating the roots:
x₁ = (-29 + 3) / 2 = -13,
x₂ = (-29 - 3) / 2 = -16.
Thus, the roots for X are -13 and -16.
Equation for Y
For the equation:
y² + 19y + 78 = 0
Again, using the quadratic formula with a = 1, b = 19, and c = 78:
Calculating the discriminant:
b² - 4ac = 19² - 4(1)(78) = 361 - 312 = 49.
Substituting back into the formula:
y = [-19 ± √49] / 2 = [-19 ± 7] / 2.
Calculating the roots:
y₁ = (-19 + 7) / 2 = -6,
y₂ = (-19 - 7) / 2 = -13.
Thus, the roots for Y are -6 and -13.
Comparing the Values
Now we can compare the maximum roots of both equations:
- Maximum root of X is -13.
- Maximum root of Y is -6.
Since -13 < -6,="" therefore:="" />
X ≤ Y
The correct answer is option 'D'.
To compare the values of X and Y from the given quadratic equations, we first need to find their roots.
Equation for X
For the equation:
x² + 29x + 208 = 0
Using the quadratic formula:
x = [-b ± √(b² - 4ac)] / 2a, where a = 1, b = 29, and c = 208.
Calculating the discriminant:
b² - 4ac = 29² - 4(1)(208) = 841 - 832 = 9.
Now, substituting back into the formula:
x = [-29 ± √9] / 2 = [-29 ± 3] / 2.
Calculating the roots:
x₁ = (-29 + 3) / 2 = -13,
x₂ = (-29 - 3) / 2 = -16.
Thus, the roots for X are -13 and -16.
Equation for Y
For the equation:
y² + 19y + 78 = 0
Again, using the quadratic formula with a = 1, b = 19, and c = 78:
Calculating the discriminant:
b² - 4ac = 19² - 4(1)(78) = 361 - 312 = 49.
Substituting back into the formula:
y = [-19 ± √49] / 2 = [-19 ± 7] / 2.
Calculating the roots:
y₁ = (-19 + 7) / 2 = -6,
y₂ = (-19 - 7) / 2 = -13.
Thus, the roots for Y are -6 and -13.
Comparing the Values
Now we can compare the maximum roots of both equations:
- Maximum root of X is -13.
- Maximum root of Y is -6.
Since -13 < -6,="" therefore:="" />
X ≤ Y
The correct answer is option 'D'.
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Community Answer
x² + 29x + 208 = 0y² + 19y + 78 = 0a)X > Yb)X < Yc)X &...
x² + 29x + 208 = 0
x = -13, -16
y² + 19y + 78 = 0
y = -13, -6
x = -13, -16
y² + 19y + 78 = 0
y = -13, -6
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