Question

x^2 - 3x - 1 = 0 , find the roots of the equation

Answer 1

GIVEN:

★$x^{2}-3x-1=0$

TO FIND:

★The zeroes of the given quadratic equation.

CONCEPT USED:

★We can find it's roots by factorisation using middle term splitting.

★We can also find it's root using standard formula

of the the equation in $ax^{2}+bx+c$ form.

i.e.$\large\green{\boxed{\dfrac{-b±\sqrt{b^{2}-4ac}}{2a}}}$

ANSWER:

We would be using here the standard formula:

We have, $x^{2}-3x-1=0$

Here • a = 1

• b = (-3)

• c = (-1)

On substituting these in formula, we have,

=$\dfrac{-b±\sqrt{b^{2}-4ac}}{2a}$

=$\dfrac{-(-3)±\sqrt{(-3)^{2}-4\times1\times(-1)}}{2\times1}$

=$\dfrac{-(-3)±\sqrt{9+4}}{2}$

=$\dfrac{3±\sqrt{13}}{2}$

=$\dfrac{3+\sqrt{13}}{2}, \dfrac{3-\sqrt{13}}{2}$

Hence the zeroes are $\dfrac{3+\sqrt{13}}{2}, \dfrac{3-\sqrt{13}}{2}$

Let $\alpha$ & $\beta$ are zeroes

$\huge\purple{\boxed{\alpha=\dfrac{3+\sqrt{13}}{2}}}$

$\huge\purple{\boxed{\beta=\dfrac{3-\sqrt{13}}{2}}}$