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If a x^2+b x+6=0 does not have distinct ...

If `a x^2+b x+6=0` does not have distinct real roots, then find the least value of `3a+bdot`

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Given, equation `ax^(2) + bx + 6 le 0, AA x in` R, if a`lt` 0
or `f(x) = ax^(2)+ bx + 6 ge 0, AA x in` R, if `gt` 0
But `f(x) = 6 gt`0
`rArr f(x) = ax^(2) + bx + 6 ge 0, AA x in` R
`rArr f(3) = 9a + 3b + 6 ge ` 0
`rArr 3a + b ge - 2`
Therefore, the least value of 3a + b`is -2.
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