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Let a , b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax2 + bx + c = 0
  • a)
    has both the roots complex
  • b)
    hat its roots lying within – 1 < x < 0
  • c)
    has one of roots equal to 1/2
  • d)
    has its roots lying within 2 < x < 6
Correct answer is option 'C'. Can you explain this answer?
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Let a , b, c be three real numbers such that a + 2b + 4c = 0. Then the...
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Let a , b, c be three real numbers such that a + 2b + 4c = 0. Then the...
To determine the nature of the roots of the equation ax^2 - bx + c = 0, let's consider the discriminant.

The discriminant (D) of a quadratic equation ax^2 - bx + c = 0 is given by D = b^2 - 4ac.

In this case, a = 1, b = -1, and c = 0.

D = (-1)^2 - 4(1)(0) = 1 - 0 = 1.

If the discriminant is positive (D > 0), the equation has two distinct real roots.
If the discriminant is zero (D = 0), the equation has one real root (a repeated root).
If the discriminant is negative (D < 0),="" the="" equation="" has="" two="" complex="" />

Since the discriminant D = 1, the equation ax^2 - bx + c = 0 has two distinct real roots.

Therefore, the correct option is:
b) has its roots lying within the real numbers.
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Let a , b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax2 + bx + c = 0a)has both the roots complexb)hat its roots lying within – 1 < x < 0c)has one of roots equal to 1/2d)has its roots lying within 2 < x < 6Correct answer is option 'C'. Can you explain this answer?
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Let a , b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax2 + bx + c = 0a)has both the roots complexb)hat its roots lying within – 1 < x < 0c)has one of roots equal to 1/2d)has its roots lying within 2 < x < 6Correct answer is option 'C'. Can you explain this answer? for 2024 is part of preparation. The Question and answers have been prepared according to the exam syllabus. Information about Let a , b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax2 + bx + c = 0a)has both the roots complexb)hat its roots lying within – 1 < x < 0c)has one of roots equal to 1/2d)has its roots lying within 2 < x < 6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let a , b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax2 + bx + c = 0a)has both the roots complexb)hat its roots lying within – 1 < x < 0c)has one of roots equal to 1/2d)has its roots lying within 2 < x < 6Correct answer is option 'C'. Can you explain this answer?.
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