Question

数学 判别式

Answer 1

(1a) (x-4p)(x-2)+p =x²-2x-4px+8p+p =x²+x(-2-4p)+9p因为y只有一个x轴截距
Δ=0 (-2-4p)²-4(1)(9p)=0 (-2)²-2(-2)(4p)+(4p)²-36p=0 4+16p+16p²-36p=0 16p²-20p+4=0 4p²-5p+1=0 (4p-1)(p-1)=0 p=1/4 或 p=1 (1b) 当p=-1/4
x²+x[-2-4(1/4)]+9(1/4)=0 x²-3x+9/4=0 4x²-12x+9=0 (2x-3)(2x-3)=0 x=3/2 当p=1 x²+x[-2-4(1)]+9(1)=0 x²-6x+9=0 (x-3)(x-3)=0 x=3 2. 请看意见栏内「㊟ 受袭猫 ㊣㊙㊡」的解答. 3.若y=9(x-1)²-m-6的图像与x轴相交
求m的最小值。 9(x-1)²-m-6 =9[x²-2(x)(1)+1²]-m-6 =9(x²-2x+1)-m-6 =9x²-18x+9-m-6 =9x²-18x+3-m因为y与x轴相交
Δ≥0 (-18)²-4(9)(3-m)≥0 324-108+36m≥0 36m≥-216 m≥-6m的最小值是-6
参考: Masterijk
12x²+4x+k=1有实根 12x²+4x+k-1=0有实根 △ ≥ 0 4² - 4*12*(k-1) ≥ 0 1 - 3*(k-1) ≥ 0 3*(k-1) ≤ 1 k-1 ≤ 1/3 k ≤ 4/3 max(k) = 4/3