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If the roots of the equation (a + b)x2 + (a + 2b + c)x + (b + c) = 0 are equal, which of the following statements is always true?
- a)a = c
- b)a + b + c = 0
- c)a = b = c
- d)b = a + c
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If the roots of the equation (a + b)x2 + (a + 2b + c)x + (b + c) = 0 ...
To find the roots of the given quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Since the roots are equal, the discriminant (b^2 - 4ac) must be equal to zero.
b^2 - 4ac = 0
Now let's substitute the coefficients from the given equation:
(a b)x^2 + (a 2b c)x + (b c) = 0
Comparing the coefficients, we have:
a b = a
a 2b c = b
b c = c
Simplifying these equations, we get:
b = 0
a 2b c = 0
b c = 0
Since b = 0, the first equation becomes:
a 0 = a
This implies that a = a, which is always true for any value of a.
Therefore, the statement "a = c" is always true when the roots of the given equation are equal.
x = (-b ± √(b^2 - 4ac)) / 2a
Since the roots are equal, the discriminant (b^2 - 4ac) must be equal to zero.
b^2 - 4ac = 0
Now let's substitute the coefficients from the given equation:
(a b)x^2 + (a 2b c)x + (b c) = 0
Comparing the coefficients, we have:
a b = a
a 2b c = b
b c = c
Simplifying these equations, we get:
b = 0
a 2b c = 0
b c = 0
Since b = 0, the first equation becomes:
a 0 = a
This implies that a = a, which is always true for any value of a.
Therefore, the statement "a = c" is always true when the roots of the given equation are equal.
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Community Answer
If the roots of the equation (a + b)x2 + (a + 2b + c)x + (b + c) = 0 ...
The discriminant of the equation is equal to zero. So, (a + 2b + c)2 = 4 ∗ (a + b)(b + c) Or (a - c)2 = 0 So, a = c
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If the roots of the equation (a + b)x2 + (a + 2b + c)x + (b + c) = 0 are equal, which of the following statements is always true?a)a = cb)a + b + c = 0c)a = b = cd)b = a + cCorrect answer is option 'A'. Can you explain this answer?
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