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If -5 is a root of the quadratic equation 2 X square bx - 15 is equal to zero and equation p X square p X 3 is equal to zero has equal roots find case?
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If -5 is a root of the quadratic equation 2 X square bx - 15 is equa...
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If -5 is a root of the quadratic equation 2 X square bx - 15 is equa...
Quadratic Equation 1: 2x² + bx - 15 = 0
Quadratic Equation 2: px² + px + 3 = 0
Given Information:
- -5 is a root of the quadratic equation 2x² + bx - 15 = 0
- The equation px² + px + 3 = 0 has equal roots
Analysis:
To find the values of 'b' and 'p', we will use the given information and apply the properties of quadratic equations.
Finding the Value of 'b':
Since -5 is a root of the equation 2x² + bx - 15 = 0, we can substitute x = -5 into the equation and solve for 'b'.
2(-5)² + b(-5) - 15 = 0
50 - 5b - 15 = 0
-5b + 35 = 0
-5b = -35
b = 7
Therefore, the value of 'b' is 7.
Finding the Value of 'p':
The equation px² + px + 3 = 0 has equal roots. This means the discriminant of this equation is zero.
The discriminant (D) of a quadratic equation ax² + bx + c = 0 is given by the formula:
D = b² - 4ac
In our equation px² + px + 3 = 0, we have a = p, b = p, and c = 3. Substituting these values into the formula for the discriminant, we have:
D = p² - 4p(3)
D = p² - 12p
Since the equation has equal roots, the discriminant is zero.
D = 0
p² - 12p = 0
p(p - 12) = 0
This equation will have equal roots when either p = 0 or p - 12 = 0.
If p = 0, the equation becomes 0x² + 0x + 3 = 0, which does not have equal roots.
If p - 12 = 0, then p = 12.
Therefore, the value of 'p' is 12.
Conclusion:
The values of 'b' and 'p' that satisfy the given conditions are b = 7 and p = 12.
Quadratic Equation 2: px² + px + 3 = 0
Given Information:
- -5 is a root of the quadratic equation 2x² + bx - 15 = 0
- The equation px² + px + 3 = 0 has equal roots
Analysis:
To find the values of 'b' and 'p', we will use the given information and apply the properties of quadratic equations.
Finding the Value of 'b':
Since -5 is a root of the equation 2x² + bx - 15 = 0, we can substitute x = -5 into the equation and solve for 'b'.
2(-5)² + b(-5) - 15 = 0
50 - 5b - 15 = 0
-5b + 35 = 0
-5b = -35
b = 7
Therefore, the value of 'b' is 7.
Finding the Value of 'p':
The equation px² + px + 3 = 0 has equal roots. This means the discriminant of this equation is zero.
The discriminant (D) of a quadratic equation ax² + bx + c = 0 is given by the formula:
D = b² - 4ac
In our equation px² + px + 3 = 0, we have a = p, b = p, and c = 3. Substituting these values into the formula for the discriminant, we have:
D = p² - 4p(3)
D = p² - 12p
Since the equation has equal roots, the discriminant is zero.
D = 0
p² - 12p = 0
p(p - 12) = 0
This equation will have equal roots when either p = 0 or p - 12 = 0.
If p = 0, the equation becomes 0x² + 0x + 3 = 0, which does not have equal roots.
If p - 12 = 0, then p = 12.
Therefore, the value of 'p' is 12.
Conclusion:
The values of 'b' and 'p' that satisfy the given conditions are b = 7 and p = 12.
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If -5 is a root of the quadratic equation 2 X square bx - 15 is equal to zero and equation p X square p X 3 is equal to zero has equal roots find case?
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If -5 is a root of the quadratic equation 2 X square bx - 15 is equal to zero and equation p X square p X 3 is equal to zero has equal roots find case? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If -5 is a root of the quadratic equation 2 X square bx - 15 is equal to zero and equation p X square p X 3 is equal to zero has equal roots find case? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If -5 is a root of the quadratic equation 2 X square bx - 15 is equal to zero and equation p X square p X 3 is equal to zero has equal roots find case?.
If -5 is a root of the quadratic equation 2 X square bx - 15 is equal to zero and equation p X square p X 3 is equal to zero has equal roots find case? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If -5 is a root of the quadratic equation 2 X square bx - 15 is equal to zero and equation p X square p X 3 is equal to zero has equal roots find case? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If -5 is a root of the quadratic equation 2 X square bx - 15 is equal to zero and equation p X square p X 3 is equal to zero has equal roots find case?.
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