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x² – 31x + 228 = 0
y² – 21y + 108 = 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 'C'. Can you explain this answer?
Verified Answer
x² – 31x + 228 = 0y² – 21y + 108 = 0a)X > Yb)...
x² – 31x + 228 = 0
x = 12, 19
y² – 21y + 108 = 0
y = 12, 9
x = 12, 19
y² – 21y + 108 = 0
y = 12, 9
Most Upvoted Answer
x² – 31x + 228 = 0y² – 21y + 108 = 0a)X > Yb)...
Quadratic Equations Analysis:
- The given equations are quadratic equations in the form ax^2 + bx + c = 0 and ay^2 + by + c = 0.
- By comparing the coefficients, we have:
- For the first equation: a = 1, b = -31, c = 228
- For the second equation: a = 1, b = -21, c = 108
Discriminant Calculation:
- The discriminant for a quadratic equation ax^2 + bx + c = 0 is given by Δ = b^2 - 4ac.
- Calculating discriminant for the first equation:
Δ1 = (-31)^2 - 4*1*228 = 961 - 912 = 49
- Calculating discriminant for the second equation:
Δ2 = (-21)^2 - 4*1*108 = 441 - 432 = 9
Relation between X and Y:
- If the discriminant is positive, the quadratic equation has two distinct real roots.
- Since both discriminants are positive, both equations have two real roots each.
- Therefore, X and Y are greater than or equal to each other, i.e., X ≥ Y.
- Hence, the correct answer is option 'C' - X ≥ Y.
In conclusion, by analyzing the given quadratic equations and calculating the discriminants, we can determine that the relationship between X and Y is such that X is greater than or equal to Y.
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x² – 31x + 228 = 0y² – 21y + 108 = 0a)X > Yb)X < Yc)X ≥ Yd)X ≤ Ye)X = Y or relation cannot be establishedCorrect answer is option 'C'. Can you explain this answer?
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