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find the estimates of x^2-x-2=3

Sagot :

Answer:

[tex]x=\frac{1+\sqrt{21}}{2}\approx 2.79\\or\ x=\frac{1-\sqrt{21}}{2}\approx -1.79[/tex]

Step-by-step explanation:

Given

Quadratic equation is

[tex]x^2-x-2=3\\x^2-x-5=0[/tex]

Roots of the quadratic equation [tex]ax^2+bx+c=0[/tex] are

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

So, for the given equation roots are

[tex]x=\frac{1\pm\sqrt{(-1)^2-4(1)(-5)}}{2\cdot 1}\\x=\frac{1\pm\sqrt{21}}{2}\\so, x=\frac{1+\sqrt{21}}{2}\approx 2.79\\or\ x=\frac{1-\sqrt{21}}{2}\approx -1.79[/tex]

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