А)у=2;-8;1/2=0.5
б)тогда ,х не принадлежит графику
![3x^2+7x-20\geq 0](https://tex.z-dn.net/?f=+3x%5E2%2B7x-20%5Cgeq+0+)
а)
Рассмотрим график функции
![y=3x^2+7x-20](https://tex.z-dn.net/?f=+y%3D3x%5E2%2B7x-20+)
это парабола, a>0 ⇒ ветви вверх
Нули функции:
![3x^2+7x-20=0\\ D=49+240=289=17^2\\ x=\dfrac{-7 \pm 17}{6} =\left[\begin{array}{I} -4 \\ \dfrac{5}{3} \end{array}}](https://tex.z-dn.net/?f=+3x%5E2%2B7x-20%3D0%5C%5C+D%3D49%2B240%3D289%3D17%5E2%5C%5C+x%3D%5Cdfrac%7B-7+%5Cpm+17%7D%7B6%7D+%3D%5Cleft%5B%5Cbegin%7Barray%7D%7BI%7D+-4++%5C%5C+%5Cdfrac%7B5%7D%7B3%7D+%5Cend%7Barray%7D%7D++)
значит функция принимает значения ≥0 при
![x \in (- \infty; \ -4] \cup [ \dfrac{5}{3}; \ + \infty)](https://tex.z-dn.net/?f=+x+%5Cin+%28-+%5Cinfty%3B+%5C+-4%5D+%5Ccup+%5B+%5Cdfrac%7B5%7D%7B3%7D%3B+%5C+%2B+%5Cinfty%29++)
Ответ: x∈(-∞; -4]U[5/3; +∞)
б)
![3x^2+7x-20\geq 0\\ 3x^2+12x-5x-20\geq 0\\ 3x(x+4)-5(x+4)\geq 0\\ (3x-5)(x+4)\geq 0](https://tex.z-dn.net/?f=+3x%5E2%2B7x-20%5Cgeq+0%5C%5C+3x%5E2%2B12x-5x-20%5Cgeq+0%5C%5C+3x%28x%2B4%29-5%28x%2B4%29%5Cgeq+0%5C%5C+%283x-5%29%28x%2B4%29%5Cgeq+0+)
![\left[\begin{array}{I} \left\{\begin{array}{I} 3x-5\geq 0 \\ x+4\geq 0\end{array}} \\ \left\{\begin{array}{I} 3x-5\leq 0\\ x+4\leq0 \end{array}} \end{array}} \ \Leftrightarrow \ \left[\begin{array}{I} \left\{\begin{array}{I} x\geq \dfrac{5}{3}\\ x\geq -4\end{array}} \\ \left\{\begin{array}{I} x\leq\dfrac{5}{3}\\ x\leq-4 \end{array}} \end{array}} \ \Leftrightarrow \ \left[\begin{array}{I} x \geq\dfrac{5}{3} \\ x\leq -4\end{array}}](https://tex.z-dn.net/?f=+%5Cleft%5B%5Cbegin%7Barray%7D%7BI%7D+%5Cleft%5C%7B%5Cbegin%7Barray%7D%7BI%7D+3x-5%5Cgeq+0+%5C%5C+x%2B4%5Cgeq+0%5Cend%7Barray%7D%7D+%5C%5C+%5Cleft%5C%7B%5Cbegin%7Barray%7D%7BI%7D+3x-5%5Cleq++0%5C%5C+x%2B4%5Cleq0+%5Cend%7Barray%7D%7D+%5Cend%7Barray%7D%7D+++%5C+%5CLeftrightarrow+%5C++%5Cleft%5B%5Cbegin%7Barray%7D%7BI%7D+%5Cleft%5C%7B%5Cbegin%7Barray%7D%7BI%7D+x%5Cgeq+%5Cdfrac%7B5%7D%7B3%7D%5C%5C+x%5Cgeq+-4%5Cend%7Barray%7D%7D+%5C%5C+%5Cleft%5C%7B%5Cbegin%7Barray%7D%7BI%7D+x%5Cleq%5Cdfrac%7B5%7D%7B3%7D%5C%5C+x%5Cleq-4+%5Cend%7Barray%7D%7D++%5Cend%7Barray%7D%7D+++++%5C+%5CLeftrightarrow+%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7BI%7D+x+%5Cgeq%5Cdfrac%7B5%7D%7B3%7D+%5C%5C+x%5Cleq+-4%5Cend%7Barray%7D%7D+++)
Ответ: x∈(-∞; -4]U[5/3; +∞)
A²-2a=6-3a
a²+a-6=0
D=1-4*(-6)=25
x=(-1+5)/2=2
x=(-1-5)/2=-3
Ответ: 2; -3