Question 18

$$\alpha$$ and $$\beta$$ are the roots of the quadratic equation $$x^2 - x - 1 = 0$$. What is the value of $$\alpha^2 + \beta^2$$?

Solution

We know ,For a quadratic equation $$ax^2+bx+c=0$$, Sum of roots= $$-\frac{b}{a}$$ and Product of roots= $$\frac{c}{a}\ .$$

So, According to question,

$$\alpha\ +\beta\ =-\frac{\left(-1\right)}{1}=1\ .$$

And, $$\alpha\beta\ =\frac{-1}{1}=-1\ .$$

So, $$\alpha^2+\beta^2=\left(\alpha\ +\beta\ \right)^2-2\alpha\beta=1-2\times\left(-1\right)=3\ .$$

A is correct choice.

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