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If minus 4 is a root of the equation X square + AX - 4 is equal to zero and the equation X square + X + b is equal to zero has equal roots the value of a and B are?
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If minus 4 is a root of the equation X square + AX - 4 is equal to zer...
Given Information:
- Minus 4 is a root of the equation X^2 + AX - 4 = 0
- The equation X^2 + X + b = 0 has equal roots
Finding the values of a and b:
Finding the Quadratic Equation:
- Since -4 is a root of X^2 + AX - 4 = 0, we can write the equation as (X + 4)(X - 1) = 0
- Expanding this gives X^2 + 3X - 4 = 0
Comparing Coefficients:
- Comparing the coefficients of X^2 and X in the given equations:
- For X^2: 1 = 1 → Coefficients are equal
- For X: A = 3 → A = 3
Using the Discriminant:
- For X^2 + X + b = 0 to have equal roots, the discriminant should be 0
- The discriminant is b^2 - 4ac = 1 - 4(b) = 0
- Solving this gives b = 1/4
Final Values:
- The value of a is 3 and the value of b is 1/4
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If minus 4 is a root of the equation X square + AX - 4 is equal to zero and the equation X square + X + b is equal to zero has equal roots the value of a and B are?
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If minus 4 is a root of the equation X square + AX - 4 is equal to zero and the equation X square + X + b is equal to zero has equal roots the value of a and B are? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If minus 4 is a root of the equation X square + AX - 4 is equal to zero and the equation X square + X + b is equal to zero has equal roots the value of a and B are? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If minus 4 is a root of the equation X square + AX - 4 is equal to zero and the equation X square + X + b is equal to zero has equal roots the value of a and B are?.
If minus 4 is a root of the equation X square + AX - 4 is equal to zero and the equation X square + X + b is equal to zero has equal roots the value of a and B are? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If minus 4 is a root of the equation X square + AX - 4 is equal to zero and the equation X square + X + b is equal to zero has equal roots the value of a and B are? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If minus 4 is a root of the equation X square + AX - 4 is equal to zero and the equation X square + X + b is equal to zero has equal roots the value of a and B are?.
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