Question

factorise x²-x-1.
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Answer 1

Answer:

Here is your answer dear

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Answer 2

Answer:

Step-by-step explanation:

Given:

A quadratic equation, $x^{2} -x-1$

To find:

Roots of given quadratic equation

Solution:

• For any equation of the form $ax^{2} + bx + c = 0$ , the roots can be found by using the formula$x = \frac{-b\pm (\sqrt[]{b^{2} -4ac}}{2a}$
• There are two possible solutions, one in which the operator adds and one in which it subtracts, as indicated by the symbol.
• Since the positive root or the negative root can be the answer when square rooting, there are always two solutions.

In the given equation, the value of $a=1 , b=-1 , c=-1$

Substituting the values in the formula,

                $x = \frac{-(-1)\pm (\sqrt[]{(-1)^{2} -4(1)(-1)}}{2(1)}$

                $x= \frac{1\pm\sqrt{1+4 }}{2}$

                 $x=\frac{1\pm\sqrt{5}}{2}$

Hence, $x=\frac{1+\sqrt{5} }{2}$    or $x=\frac{1-\sqrt{5} }{2}$

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