Question

If the quadratic equation `a x^2+b x+6=0` does not have real roots and `b in R^+` , then prove that `a > m a x{(b^2)/(24),b-6}`

Answer 1

For the equation `ax^(2) + bx + 6 = 0` , roots are not real. Hence,
` D lt 0 rArr b^(2) - 24 a lt 0 or a gt (b^(2))/(24)`
Also, `f(0) = 6 gt 0 `. So ,
` f (-1) gt 0 rArr a + b + 6 gt 0`
`rArr a gt max {(b^(2))/(24), b -c}`.