InterviewSolution
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InterviewSolution
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If `x`is real and the roots of the equation `a x^2+b x+c=0`are imaginary, then prove tat `a^2x^2+a b x+a c`is always positive. |
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Answer» Correct Answer - ` a in ( infty), -2)` Given, roots of `ax^(2) + bx + c = 0` are imaginary . Hence, ` b^(2) - 4ac lt 0 ` (1) Let us consider `f(x) = a^(2) x^(2) + abx + ac `. Her, coefficient of f(x) is `a^(2)` which is + ve, which makes graph concave upward. Also, ` D = (ab)^(2) - 4a^(2) (ac) = a^(2) (b^(2) - 4ac) lt 0` Hence, `f(x) gt 0 , AA x in ` R . |
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