2) one minimum value 3) no extreme value 4) one maximum and one minimum value Solution (3) no extreme value f (x) = x 3 ax 2 bx c, a 2 = 3b f' (x) = 3x 2 2ax b Put f' (x) = 0 3x 2 2ax b = 0 x = 2a ± √4a 2 – 12b / 2 * 3 = 2a ± √a 2 – 3b / 3 Since, a 2 = 3b, x has an imaginary value So, no extreme The quartic polynomial $f(x) = x^4 a x^3 b x^2 c x d$ is such that $ad$ is odd and $bc$ is even Prove that $f(x)$ does not has all rational rootsLet us calculate the derivative of F(X) F'(X)= 3X²2AXB Now since it doesn't depend upon C, hence C can take any value present on a dice (1 to 6) Now F'(X) should be always greater than 0 for F(X) to be increasing function For this quadratic equation to be greater than zero for all X, the discriminant D has to be negative
If One Of The Zeroes Of The Cubic Polynomial X 3 Ax 2 Bx C Is 1 Then The Product Of The Other Two Zeroes Is A B A 1 B B A 1 C A B 1 D A B 1 Snapsolve
