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If two equations: 2x2 - Ax - 20 = 0 and 2x2 - 11x + 12 = 0 have one root in common, then what is the value of 'A' if the value of A is positive?
- a)3
- b)2
- c)4
- d)5
Correct answer is option 'A'. Can you explain this answer?
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If two equations: 2x2 - Ax - 20 = 0 and 2x2 - 11x + 12 = 0 have one r...
2x2 - 11x + 12 = 0
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(2x - 3)(x - 4) = 0
x = 1.5 and 4
Since both the equations have one root in common-
Case 1: When x = 1.5 is common-
2(1.5)2 - A(1.5) - 20 = 0
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If two equations: 2x2 - Ax - 20 = 0 and 2x2 - 11x + 12 = 0 have one r...
To find the value of 'A' when the two equations have one root in common, we can set the discriminants of the equations equal to zero and solve for 'A'.
1. Discriminant of the first equation:
The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by Δ = b^2 - 4ac. In the first equation, a = 2, b = -A, and c = -20.
So, the discriminant of the first equation is Δ1 = (-A)^2 - 4(2)(-20) = A^2 + 160.
2. Discriminant of the second equation:
In the second equation, a = 2, b = -11, and c = 12.
So, the discriminant of the second equation is Δ2 = (-11)^2 - 4(2)(12) = 121 - 96 = 25.
Since the two equations have one root in common, the discriminants Δ1 and Δ2 must be equal to zero.
3. Setting the discriminants equal to zero:
Δ1 = A^2 + 160 = 0
Δ2 = 25 = 0
4. Solving for 'A':
From Δ2 = 25, we can see that it is not possible for the discriminant of a quadratic equation to be zero. Therefore, the second equation does not have one root in common with the first equation.
As a result, 'A' does not have a positive value that satisfies the condition of the problem. Therefore, none of the given options (a), b), c), d)) is correct.
In conclusion, the correct answer cannot be determined as the given information contradicts the condition that the two equations have one root in common.
1. Discriminant of the first equation:
The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by Δ = b^2 - 4ac. In the first equation, a = 2, b = -A, and c = -20.
So, the discriminant of the first equation is Δ1 = (-A)^2 - 4(2)(-20) = A^2 + 160.
2. Discriminant of the second equation:
In the second equation, a = 2, b = -11, and c = 12.
So, the discriminant of the second equation is Δ2 = (-11)^2 - 4(2)(12) = 121 - 96 = 25.
Since the two equations have one root in common, the discriminants Δ1 and Δ2 must be equal to zero.
3. Setting the discriminants equal to zero:
Δ1 = A^2 + 160 = 0
Δ2 = 25 = 0
4. Solving for 'A':
From Δ2 = 25, we can see that it is not possible for the discriminant of a quadratic equation to be zero. Therefore, the second equation does not have one root in common with the first equation.
As a result, 'A' does not have a positive value that satisfies the condition of the problem. Therefore, none of the given options (a), b), c), d)) is correct.
In conclusion, the correct answer cannot be determined as the given information contradicts the condition that the two equations have one root in common.
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If two equations: 2x2 - Ax - 20 = 0 and 2x2 - 11x + 12 = 0 have one root in common, then what is the value of 'A' if the value of A is positive?a)3b)2c)4d)5Correct answer is option 'A'. Can you explain this answer?
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