Question

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

Answer 1

Answer:

$x=\frac{1+\sqrt{21}}{2}\approx 2.79\\or\ x=\frac{1-\sqrt{21}}{2}\approx -1.79$

Step-by-step explanation:

Given

Quadratic equation is

$x^2-x-2=3\\x^2-x-5=0$

Roots of the quadratic equation $ax^2+bx+c=0$ are

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

So, for the given equation roots are

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