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数学 高校生

(2)が下の解答を読んでも分かりません。 特に、求める条件がなぜ①、②になるのか分かりません。 解説お願いします。

すべての実数で成り立つ不等式 CS 例題 79 次の条件を満たすような定数kの値の範囲を求めよ. 野 V (1) すべての実数xに対して, 不等式 x2+kx+k+30 が成り立つ. J (2) 2次不等式 kx²+(k+3)x+k > 0 が解をもたない。 グラフが上に凸か下に凸かを調べ,x軸との位置関係に着目する (8) TO 与えられた2次不等式において, (左辺)=0としたとき の判別式をDとする. (1) 2次関数y=x2+kx+ のグラフが右の図のようになる ときを考えると,求める条件は、 「 (2次の係数)>0 ・① {6² \D=k²-4(k+3) <0.2 ① は成り立つ. XJ 2, k²-4(k+3) <0 k²-4k-12<0 考え方 解答 y=x²+kx+k+3 Med ②より k≦-1.3≦k これと①より, k≦-1 GIST 分身 (k+2)(k-6) <0より。 よって, 求めるんの値の範囲は、 (2) kx2+(k+3)x+k > 0 が解をもたない ⇔ すべてのxで kx²+(k +3)x+k≦0 k=0 次不等式であるから, よって, 求める条件は, 「2次の係数 k<0 ...1 \D=(k+3)²-4k² ≤02 x -1-50+53-16-(8+) -2<k<6_D 2<k<6 (4-08)-³ (0- **** すべての実数で成り 立つ 解はすべての y=kx²+(k+3)x+k x S+ 調べなくてよい. 2次関数のグ ラフは下に凸でx軸 と共有点をもたない ⇒ a > 0, D< 0 2次不等式とあるの でん=0 の場合は |第2 ¥2 (頂点のy座標)≦0 牛 つまり, としてもよ 3(k²-2k-3) -≤0 4k でもよいが計算が煩 雑となるため、Dを 用いる.

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英語 高校生

仮定法の範囲です! 6〜21、20、24〜26の答えあってるか確認して欲しいです!不正解の場合正しい回答も教えてくれると助かります🙇‍♂️

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