Question

Find the roots of x2-3x-1=0 by using quadratic formula

Answer 1

Hey friend, Here is your answer-

Here , a = 1 , b = -3 , c = -1

b^2-4ac = (-3)^2 - 4 × 1 × (-1)

= 9 + 4

= 13

x = -b +/- root b2-4ac / 2a

x = 3 +/- root 13 / 2

Therefore ,

$x = \frac{3 - \sqrt{13} }{2} \\ or \\ x = \frac{3 + \sqrt{13} }{2}$

Hope it will help you.

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Answer 2

Quadratic equation is

=>$x^2$-3x-1=0

ANSWER

Now to solve a quadratic equation we can use 3 methods =>

1)Completing the Square Method,

2)Middle term Split method, and

3)By Quadratic formula.

Here we will be using the quadratic formula method --->

d=$b^2$- 4×a ×c

=>d = $(-3)^2$ - {4 × 1×(-1)}

=>d = 9 + 4

=>d = 13.

Since d>0

hence the equation has 2 real and distinct roots.

Hence,

x = $\dfrac{-b\pm \sqrt{d}}{2\times{a}}$

=>x = $\dfrac{3\pm\sqrt{13}}{2\times{1}}$

So, we get=>

Either

x= $\dfrac{3 + \sqrt{13}}{2}$

or

x = $\dfrac{3 - \sqrt{13}}{2}$

REMEMBER

Remember

In quadratic formula

$X = \dfrac{-b\pm\sqrt{d}}{2\times{a}}$

and

d is discriminant which determines the nature of roots