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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...
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c)has both the roots negative
d)has at least one root negative and at least one root positive
We can rewrite the given condition as a = -2b/4c, which simplifies to a = -b/2c. Substituting this value of a in the quadratic equation, we get:
(-b/2c)x^2 + bx - c = 0
Multiplying both sides by -2c and simplifying, we get:
bx^2 - 2cx + 2b = 0
Now we can apply the quadratic formula to find the roots:
x = [2c ± √(4c^2 - 8b)] / 2b
Simplifying further, we get:
x = [c ± √(c^2 - 2b)] / b
Since b and c are both real numbers, we can see that the discriminant (c^2 - 2b) can be either positive, zero or negative.
If the discriminant is positive, then both roots will be real and have opposite signs (one positive and one negative).
If the discriminant is zero, then both roots will be equal and real.
If the discriminant is negative, then both roots will be complex conjugates of each other and have negative real part.
Therefore, the correct answer is (a) has both the roots complex.
c)has both the roots negative
d)has at least one root negative and at least one root positive
We can rewrite the given condition as a = -2b/4c, which simplifies to a = -b/2c. Substituting this value of a in the quadratic equation, we get:
(-b/2c)x^2 + bx - c = 0
Multiplying both sides by -2c and simplifying, we get:
bx^2 - 2cx + 2b = 0
Now we can apply the quadratic formula to find the roots:
x = [2c ± √(4c^2 - 8b)] / 2b
Simplifying further, we get:
x = [c ± √(c^2 - 2b)] / b
Since b and c are both real numbers, we can see that the discriminant (c^2 - 2b) can be either positive, zero or negative.
If the discriminant is positive, then both roots will be real and have opposite signs (one positive and one negative).
If the discriminant is zero, then both roots will be equal and real.
If the discriminant is negative, then both roots will be complex conjugates of each other and have negative real part.
Therefore, the correct answer is (a) has both the roots complex.
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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?.
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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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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
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