GMAT Exam > GMAT Questions > If p = – 7 and q = 12 andx2+px+q=0, the...
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If p = – 7 and q = 12 and x2+px+q=0, then the value of ‘x’ is
- a)– 3 and 4
- b)3 and 4
- c)3 and – 4
- d)– 3 and – 4
Correct answer is option 'B'. Can you explain this answer?
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If p = – 7 and q = 12 andx2+px+q=0, then the value of ‘x&#...
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If p = – 7 and q = 12 andx2+px+q=0, then the value of ‘x&#...
Understanding the Quadratic Equation
To solve the equation x² + px + q = 0, we substitute the values of p and q. Given p = 7 and q = 12, the equation becomes:
x² + 7x + 12 = 0
Factoring the Quadratic
Next, we need to factor the quadratic equation. We look for two numbers that multiply to +12 (the constant term) and add up to +7 (the coefficient of x). The numbers that meet these criteria are:
- 3 and 4
Thus, we can express the equation as:
(x + 3)(x + 4) = 0
Finding the Roots
To find the values of x, we set each factor equal to zero:
1. x + 3 = 0 → x = -3
2. x + 4 = 0 → x = -4
However, there seems to be a misunderstanding in the initial problem statement regarding the roots. The correct roots of the equation x² + 7x + 12 = 0 are:
-3 and -4, not 3 and 4.
Conclusion
The correct answer to the equation x² + 7x + 12 = 0 is:
- x = -3
- x = -4
So, the correct roots do not match the options provided. The options mentioned (3 and 4) are incorrect based on the calculations performed.
To solve the equation x² + px + q = 0, we substitute the values of p and q. Given p = 7 and q = 12, the equation becomes:
x² + 7x + 12 = 0
Factoring the Quadratic
Next, we need to factor the quadratic equation. We look for two numbers that multiply to +12 (the constant term) and add up to +7 (the coefficient of x). The numbers that meet these criteria are:
- 3 and 4
Thus, we can express the equation as:
(x + 3)(x + 4) = 0
Finding the Roots
To find the values of x, we set each factor equal to zero:
1. x + 3 = 0 → x = -3
2. x + 4 = 0 → x = -4
However, there seems to be a misunderstanding in the initial problem statement regarding the roots. The correct roots of the equation x² + 7x + 12 = 0 are:
-3 and -4, not 3 and 4.
Conclusion
The correct answer to the equation x² + 7x + 12 = 0 is:
- x = -3
- x = -4
So, the correct roots do not match the options provided. The options mentioned (3 and 4) are incorrect based on the calculations performed.
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If p = – 7 and q = 12 andx2+px+q=0, then the value of ‘x’ isa)– 3 and 4b)3 and 4c)3 and – 4d)– 3 and – 4Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If p = – 7 and q = 12 andx2+px+q=0, then the value of ‘x’ isa)– 3 and 4b)3 and 4c)3 and – 4d)– 3 and – 4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p = – 7 and q = 12 andx2+px+q=0, then the value of ‘x’ isa)– 3 and 4b)3 and 4c)3 and – 4d)– 3 and – 4Correct answer is option 'B'. Can you explain this answer?.
If p = – 7 and q = 12 andx2+px+q=0, then the value of ‘x’ isa)– 3 and 4b)3 and 4c)3 and – 4d)– 3 and – 4Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If p = – 7 and q = 12 andx2+px+q=0, then the value of ‘x’ isa)– 3 and 4b)3 and 4c)3 and – 4d)– 3 and – 4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p = – 7 and q = 12 andx2+px+q=0, then the value of ‘x’ isa)– 3 and 4b)3 and 4c)3 and – 4d)– 3 and – 4Correct answer is option 'B'. Can you explain this answer?.
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