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The roots of a quadratic equation x2−4px+4p2−q2=0 are
- a)p + 2q, p – 2q
- b)2p + q, 2p – q
- c)2p + q, 2p + q
- d)2p – q, 2p – q
Correct answer is option 'B'. Can you explain this answer?
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The roots of a quadratic equationx2−4px+4p2−q2=0area)p + 2...
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The roots of a quadratic equationx2−4px+4p2−q2=0area)p + 2...
The roots of a quadratic equation can be found using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
The discriminant, b^2 - 4ac, determines the nature of the roots:
- If the discriminant is positive, then there are two real roots.
- If the discriminant is zero, then there is one real root (which is also called a double root).
- If the discriminant is negative, then there are two complex roots (which are conjugates of each other).
For example, consider the quadratic equation x^2 + 4x + 4 = 0. Here, a = 1, b = 4, and c = 4. Plugging these values into the quadratic formula gives:
x = (-4 ± √(4^2 - 4(1)(4))) / 2(1)
x = (-4 ± 0) / 2
x = -2
So the equation has one real root, x = -2.
x = (-b ± √(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
The discriminant, b^2 - 4ac, determines the nature of the roots:
- If the discriminant is positive, then there are two real roots.
- If the discriminant is zero, then there is one real root (which is also called a double root).
- If the discriminant is negative, then there are two complex roots (which are conjugates of each other).
For example, consider the quadratic equation x^2 + 4x + 4 = 0. Here, a = 1, b = 4, and c = 4. Plugging these values into the quadratic formula gives:
x = (-4 ± √(4^2 - 4(1)(4))) / 2(1)
x = (-4 ± 0) / 2
x = -2
So the equation has one real root, x = -2.
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The roots of a quadratic equationx2−4px+4p2−q2=0area)p + 2q, p – 2qb)2p + q, 2p – qc)2p + q, 2p + qd)2p – q, 2p – qCorrect answer is option 'B'. Can you explain this answer?
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The roots of a quadratic equationx2−4px+4p2−q2=0area)p + 2q, p – 2qb)2p + q, 2p – qc)2p + q, 2p + qd)2p – q, 2p – qCorrect 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 The roots of a quadratic equationx2−4px+4p2−q2=0area)p + 2q, p – 2qb)2p + q, 2p – qc)2p + q, 2p + qd)2p – q, 2p – qCorrect 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 The roots of a quadratic equationx2−4px+4p2−q2=0area)p + 2q, p – 2qb)2p + q, 2p – qc)2p + q, 2p + qd)2p – q, 2p – qCorrect answer is option 'B'. Can you explain this answer?.
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