(a) Solve the quadratic equation $2 x^{2}+5 x-2=0$ analytically. Give the solutions in exact form.
(b) Graph $P(x)=2 x^{2}+5 x-2$ with a calculator. Use your results in part (a) along with this graph to give the solution set of each inequality. Express endpoints of the intervals in exact form.
(i) $P(x)0$
(ii) $P(x) \leq 0$

Question

(a) Solve the quadratic equation $2 x^{2}+5 x-2=0$ analytically. Give the solutions in exact form.
(b) Graph $P(x)=2 x^{2}+5 x-2$ with a calculator. Use your results in part (a) along with this graph to give the solution set of each inequality. Express endpoints of the intervals in exact form.
(i) $P(x)>0$
(ii) $P(x) \leq 0$

Quizplus · Accepted Answer

The Answer is (a)

\left\{\frac{-5 \pm 1 \overline{41}}{4}\right\}

(b)
$(a) \left\{\frac{-5 \pm 1 \overline{41}}{4}\right\} (b) (i) \left(-\infty, \frac{-5-\sqrt{41}}{4}\right) \cup\left(\frac{-5+\sqrt{41}}{4}, \infty\right) (ii) \left[\frac{-5-\sqrt{41}}{4}, \frac{-5+\sqrt{41}}{4}\right]$ (i)

\left(-\infty, \frac{-5-\sqrt{41}}{4}\right) \cup\left(\frac{-5+\sqrt{41}}{4}, \infty\right)

(ii)

\left[\frac{-5-\sqrt{41}}{4}, \frac{-5+\sqrt{41}}{4}\right]

(A) Solve the Quadratic Equation 2x2+5x−2=02 x^{2}+5 x-2=02x2+5x−2=0 Analytically P(x)=2x2+5x−2P(x)=2 x^{2}+5 x-2P(x)=2x2+5x−2

(A) Solve the Quadratic Equation $2 x^{2}+5 x-2=0$ Analytically $P(x)=2 x^{2}+5 x-2$