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Suppose a, b denote the distinct real roots of the quadratic polynomial x2 + 20x – 2020 and suppose c,d denote the distinct complex roots of the quadratic polynomial x2 – 20x + 2020. Then the value of ac(a – c) + ad(a – d) + bc(b – c) + bd(b – d) is
  • a)
    0
  • b)
    8000
  • c)
    8080
  • d)
    16000
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Suppose a, b denote the distinct real roots of the quadratic polynomia...
To find the roots of the quadratic polynomial x^2 - 20x + ab, we can use the quadratic formula.

The quadratic formula states that for a quadratic equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, a = 1, b = -20, and c = ab. Plugging these values into the quadratic formula, we have:

x = (-(-20) ± √((-20)^2 - 4(1)(ab))) / (2(1))
x = (20 ± √(400 - 4ab)) / 2
x = (20 ± √(400 - 4ab)) / 2
x = 10 ± √(100 - ab)

Since a and b are distinct real roots, we can assume that ab ≠ 100, otherwise a and b would be the same. Therefore, we can simplify the expression further:

x = 10 ± √(100 - ab)

So, the distinct real roots of the quadratic polynomial x^2 - 20x + ab are 10 + √(100 - ab) and 10 - √(100 - ab).
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Suppose a, b denote the distinct real roots of the quadratic polynomial x2 + 20x – 2020 and suppose c,d denote the distinct complex roots of the quadratic polynomial x2 – 20x + 2020. Then the value ofac(a – c) + ad(a – d) + bc(b – c) + bd(b – d)isa)0b)8000c)8080d)16000Correct answer is option 'D'. Can you explain this answer?
Question Description
Suppose a, b denote the distinct real roots of the quadratic polynomial x2 + 20x – 2020 and suppose c,d denote the distinct complex roots of the quadratic polynomial x2 – 20x + 2020. Then the value ofac(a – c) + ad(a – d) + bc(b – c) + bd(b – d)isa)0b)8000c)8080d)16000Correct answer is option 'D'. 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 Suppose a, b denote the distinct real roots of the quadratic polynomial x2 + 20x – 2020 and suppose c,d denote the distinct complex roots of the quadratic polynomial x2 – 20x + 2020. Then the value ofac(a – c) + ad(a – d) + bc(b – c) + bd(b – d)isa)0b)8000c)8080d)16000Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose a, b denote the distinct real roots of the quadratic polynomial x2 + 20x – 2020 and suppose c,d denote the distinct complex roots of the quadratic polynomial x2 – 20x + 2020. Then the value ofac(a – c) + ad(a – d) + bc(b – c) + bd(b – d)isa)0b)8000c)8080d)16000Correct answer is option 'D'. Can you explain this answer?.
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