Find the 20

Find the product and the sum of the roots of x² + 3x - 9 = 0

Correct answer:

p =  -9
s =  -3

Step-by-step explanation:

$$\begin{gathered} x^2+3x-9=0 \\ a=1 \\ b=3 \\ c=-9 \\ p=c\mathrm{/}a=(-9)\mathrm{/}1=-9 \end{gathered}$$

$$\begin{gathered} s=-b\mathrm{/}a=-3\mathrm{/}1=-3 \\ \text{ Verifying Solution: } \\ {x}^2+3x-9=0 \\ {x}^2+3x-9=0 \\ a=1;b=3;c=-9 \\ D=b^2-4ac=3^2-4\cdot 1\cdot (-9)=45 \\ D>0 \\ {x}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{-3\pm \sqrt{45}}{2}}={\displaystyle \frac{-3\pm 3\sqrt{5}}{2}} \\ {x}_{1,2}=-1.5\pm 3.3541019662497 \\ {x}_1=1.8541019662497 \\ {x}_2=-4.8541019662497 \\ \text{ Factored form of the equation: } \\ (x-1.8541019662497)(x+4.8541019662497)=0 \\ {p}_1=x_1\cdot x_2=1.8541\cdot (-4.8541)=-9 \\ {s}_1=x_1+x_2=1.8541+(-4.8541)=-3 \end{gathered}$$

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