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If both roots of the quadratic equation
(2 – x) (x + 1) = p are distinct & positive, then p must lie in the interval
- a)(2, ¥)
- b)(2, 9/4)
- c)(–¥, –2)
- d)(–¥, ¥)
Correct answer is option 'B'. Can you explain this answer?
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If both roots of the quadratic equation(2 –x) (x + 1) = p are di...
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If both roots of the quadratic equation(2 –x) (x + 1) = p are di...
If both roots of the quadratic equation are equal, then the discriminant, denoted as Δ, must be equal to zero. The discriminant is given by the formula Δ = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
In this case, since both roots are equal, we can write the quadratic equation as (x - r)(x - r) = 0, where r is the common root.
Expanding this equation, we have x^2 - 2rx + r^2 = 0.
Comparing this with the standard form of a quadratic equation, we can see that a = 1, b = -2r, and c = r^2.
Substituting these values into the discriminant formula, we get Δ = (-2r)^2 - 4(1)(r^2).
Simplifying this expression, we have Δ = 4r^2 - 4r^2 = 0.
Therefore, if both roots of the quadratic equation are equal, the discriminant will be equal to zero.
In this case, since both roots are equal, we can write the quadratic equation as (x - r)(x - r) = 0, where r is the common root.
Expanding this equation, we have x^2 - 2rx + r^2 = 0.
Comparing this with the standard form of a quadratic equation, we can see that a = 1, b = -2r, and c = r^2.
Substituting these values into the discriminant formula, we get Δ = (-2r)^2 - 4(1)(r^2).
Simplifying this expression, we have Δ = 4r^2 - 4r^2 = 0.
Therefore, if both roots of the quadratic equation are equal, the discriminant will be equal to zero.
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If both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. Can you explain this answer?
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If both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. Can you explain this answer?.
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