If the image of quadratic function y = (M + 5) x2 + 2 (M + 1) x + m is all above the x-axis, then the value range of M is___ .

If the image of quadratic function y = (M + 5) x2 + 2 (M + 1) x + m is all above the x-axis, then the value range of M is___ .

∵ the images of quadratic function y = (M + 5) x2 + 2 (M + 1) x + m are all above the x-axis, ∵ (M + 5) > 0, ∵ 0, ∵ m > - 5, 4 (M + 1) 2-4 (M + 5) × m < 0, so m > 13