InterviewSolution
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InterviewSolution
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If the roots of the equation `a x^2+b x+c=0`are of the form `(k+1)//ka n d(k+2)//(k+1),t h e n(a+b+c)^2`is equal to`2b^2-a c`b. `a 62`c. `b^2-4a c`d. `b^2-2a c`A. `2b^(2) - ac`B. `a^(2)`C. `b^(2) - 4ac`D. `b^(2) - 2ac` |
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Answer» Correct Answer - 3 We have `(k + 1)/(k) + (k + 2)/(k + 1) = - b/a" "(1)` and `(k + 1)/(k) (k + 2)/(k + 1) = c/a` `rArr (k + 2)/(k) = c/a` or `2/k = c/a - 1 = (c - a)/(a)` or `k = (2a)/(c - a)" "(2)` Now, eliminate k. Putting the value of k in Eq. (1), we get `(c + a)/(2a) + (2c)/(c + a) = -b/a` or `(c + a)^(2) + 4ac = -2b (a + c)` or `(a + c)^(2) + 2b (a + c) = -4ac` Adding `b^(2)` to both sides, we have `(a + b + c)^(2) = b^(2) - 4ac` |
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