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$Q:$\Rightarrow$ Find the least positive Integral value of $a$ for which the equation\\\\ $3x^4+4x^3-12x^2+5a=0$ has no real roots.
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3 Answers
1063x4 + 9x3 - 4x3 -12x2 +5a = 0
=> (3x3 - 4x2)(x+3) + 5a = 0
=> x2(3x-4)(x+3) = -5a
Consider graph of y= x2(3x-4)(x+3)
find the min. value of dis.
find the least positive value to be added so that the graph just touches x-axis at one / two points.. (hvnt calculated)...and hence calculate 'a' which is the least positive 'integral' value.
21the function F(x)= 3x^4 + 4x^3 - 12x^2 ,at x=0,1 and -2 the slope is zero///
the value at x=2 is -32 and it is the minimum value...so the min value of a =7