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22 Apr 2019, 12:01
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
65% (02:30) correct
35%
(02:21)
wrong
based on 335
sessions
History
Date
Time
Result
Not Attempted Yet
One of the two students while solving a quadratic equation in x copied the constant term incorrectly and got his roots as 3,2 .The other copied the the constant and coefeicent term of \(x^{2}\) correctly as -6, 1 respectively . The correct roots of the equation are ?
(A)3,-2
(B)-3,2
(C)3,3
(D)-6,-1
(E)6,-1
(A)3,-2
(B)-3,2
(C)3,3
(D)-6,-1
(E)6,-1
22 Apr 2019, 19:01
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For a quadratic equation a\(x^{2}\)+ bx + c = 0, sum of roots = -b/a and product of roots = c/a
Given that one student copied the the constant and coefficient term of \(x^{2}\) correctly as -6, 1 respectively.
Product of roots = c/a = constant term/coefficient term of \(x^{2}\)
Product of the roots = -6/1 = -6
Also, another student copied the constant term incorrectly and got his roots as 3, 2. However, the constant term has no bearing on the sum of roots.
Therefore the sum of roots = 3 + 2 = 5
Of the 5 answer choices, only answer option E satisfies both the conditions, i.e. the product of roots is -6 and the sum of roots is 5. Therefore, the correct answer is option E. 6, -1
Given that one student copied the the constant and coefficient term of \(x^{2}\) correctly as -6, 1 respectively.
Product of roots = c/a = constant term/coefficient term of \(x^{2}\)
Product of the roots = -6/1 = -6
Also, another student copied the constant term incorrectly and got his roots as 3, 2. However, the constant term has no bearing on the sum of roots.
Therefore the sum of roots = 3 + 2 = 5
Of the 5 answer choices, only answer option E satisfies both the conditions, i.e. the product of roots is -6 and the sum of roots is 5. Therefore, the correct answer is option E. 6, -1
29 Nov 2020, 13:08
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Probus
For the first equation, he copied the constant term incorrectly which means he got the coefficient of the x term and \(x^2\) term correct. In the standard quadratic equation form, the coefficient of the x term is the negative sum of the roots. So the coefficient of the x term is \((-5)/1 = -5\), where 1 is the coefficient of the \(x^2\) term.
Combining with the second sentence we know the entire quadratic equation is \(x^2 -5x -6 = 0\), or \((x - 6)(x + 1)\) so the solutions are 6 and -1.
Ans: E
