Question

2. Determine the number of real roots y = -x^2 - 4x + 3 has. Justify your answer.

Answer 1

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Real roots

y = -x^2 - 4x + 3

0 = x^2 + 4 -3

Using the quadratic formula

a= 1

b= 4

c= -3

`x=\text{ }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

`x=\text{ }\frac{-4\pm\sqrt[]{4^2-4\cdot1\cdot(-3)}}{2\cdot1}=\text{ }\frac{-4\pm\sqrt[]{16+12}}{2}=\text{ }\frac{-4\pm\sqrt[]{28}}{2}=\text{ }\frac{-4\pm\sqrt[]{7\cdot4}}{2}=\text{ }\frac{-4\pm2\sqrt[]{7}}{2}=\text{ }-2\pm\sqrt[]{7}`

x1= -2 + √7

x2= -2 - √7

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Answer

x1= -2 + √7

x2= -2 - √7