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The quadratic equation x2 + bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of b2 + c?
- a)3721
- b)361
- c)427
- d)549
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The quadratic equation x2 + bx + c = 0 has two roots 4a and 3a, where...
Given, The quadratic equation x2 + bx + c = 0 has two roots 4a and 3a
View all questions of this test
7a=-b
12a2 = c
We have to find the value of b2 + c = 49a2+ 12a2=61a2
Now let’s verify the options
61 a2 = 3721 ==> a= 7.8 which is not an integer
61 a2 = 361 ==> a= 2.42 which is not an integer
61 a2 = 427 ==> a= 2.64 which is not an integer
61 a2 = 3721 ==> a= 3 which is an integer
Most Upvoted Answer
The quadratic equation x2 + bx + c = 0 has two roots 4a and 3a, where...
To find the value of b^2 - c, we need to first find the values of b and c. Given that the quadratic equation has two roots 4a and 3a, we can write the equation as:
(x - 4a)(x - 3a) = 0
Expanding this equation, we get:
x^2 - 7ax + 12a^2 = 0
Comparing this equation with the given quadratic equation x^2 + bx + c = 0, we can equate the coefficients:
b = -7a
c = 12a^2
Now, we need to find the value of b^2 - c. Substituting the values of b and c, we get:
b^2 - c = (-7a)^2 - 12a^2
= 49a^2 - 12a^2
= 37a^2
Therefore, the value of b^2 - c is 37a^2.
Since a is an integer, the value of 37a^2 will be a perfect square only when a = 3. Substituting a = 3, we get:
37(3)^2 = 333
Therefore, the possible value of b^2 - c is 333.
Hence, the correct answer is option D) 549.
(x - 4a)(x - 3a) = 0
Expanding this equation, we get:
x^2 - 7ax + 12a^2 = 0
Comparing this equation with the given quadratic equation x^2 + bx + c = 0, we can equate the coefficients:
b = -7a
c = 12a^2
Now, we need to find the value of b^2 - c. Substituting the values of b and c, we get:
b^2 - c = (-7a)^2 - 12a^2
= 49a^2 - 12a^2
= 37a^2
Therefore, the value of b^2 - c is 37a^2.
Since a is an integer, the value of 37a^2 will be a perfect square only when a = 3. Substituting a = 3, we get:
37(3)^2 = 333
Therefore, the possible value of b^2 - c is 333.
Hence, the correct answer is option D) 549.
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The quadratic equation x2 + bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of b2 + c?a) 3721b) 361c) 427d) 549Correct answer is option 'D'. Can you explain this answer?
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