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Question 9
The quadratic equation $$x^2 + bx + c = 0$$ has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of $$b^2 + c$$?
Solution
Given,
The quadratic equation $$x^2 + bx + c = 0$$ has two roots 4a and 3a
7a=-b
12$$a^2$$ = c
We have to find the value of $$b^2 + c$$ = 49$$a^2$$+ 12$$a^2$$=61$$a^2$$
Now lets verify the options
61$$a^2$$ = 3721 ==> a= 7.8 which is not an integer
61$$a^2$$ = 361 ==> a= 2.42 which is not an integer
61$$a^2$$ = 427 ==> a= 2.64 which is not an integer
61$$a^2$$ = 549 ==> a= 3 which is an integer
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