(a) 求使方程 $8x^2+kx+2=0$ 没有实根的 $k$ 的取值集合。

(b) 解方程 $8\cos^2\theta-10\cos\theta+2=0$，其中 $0^\circ\leq\theta\leq180^\circ$。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

二次方程没有实根时，判别式严格小于零。

The discriminant is $k^2-4(8)(2)=k^2-64$. It is negative exactly when $-8<k<8$. The endpoints are excluded because the quadratic then has a repeated real root.

令 $u=\cos\theta$，因式分解后在给定半周内逐一找角。

The equation factors as $2(4\cos\theta-1)(\cos\theta-1)=0$. Thus $\cos\theta=1$ or $1/4$, giving $\theta=0^\circ$ or $75.5^\circ$ to one decimal place where rounding is needed.