Question

find roots of x²+5x+5=0 by quadratic formula​

Answer 1

A Quadratic Equation

$\sf x^2+5x+5=0$

We have to find the roots of given equation

• By using quadratic formula

$\boxed{\sf{x= \dfrac{-b\pm\sqrt{b{}^{2}-4ac}}{2a}}}$

Now we have ,

Coefficient of $\sf x^2$(a) = 1

Coefficient of x (b) = 5

Constant term (c) = 5

Now find the roots

$\sf\bullet a= 1\ \ , \ \bullet \ b= 5 \ \ , \ \bullet\ c= 5$

$\longmapsto\sf x= \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\ \\ \\ \longmapsto\sf x= \dfrac{-5\pm \sqrt{(5)^2-4\times 1\times 5}}{2\times 1}\\ \\ \\ \longmapsto\sf x= \dfrac{-5 \pm \sqrt{25-20}}{2}\\ \\ \\ \longmapsto\sf x= \dfrac{-5\pm \sqrt{5}}{2}\\ \\ \\ \longmapsto\sf x = \dfrac{-5-\sqrt{5}}{2} \ \ or \ \dfrac{-5+\sqrt{5}}{2}$

So the roots of given equation is

$\bigstar{\boxed{\sf{ \dfrac{-5-\sqrt{5}}{2}}}}$

$\bigstar{\boxed{\sf{ \dfrac{-5+\sqrt{5}}{2}}}}$

Answer 2

${\underline{\huge{\mathbf{\color{pink}{question}}}}}$

find roots of $x^2+5x+5 = 0$by quadratic formula

________________________❤

${\underline{\huge{\mathbf{\color{pink}{solution}}}}}$

• equation

$\sf x^2+5x+5=0$

• quadratic formula

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

• finding value of a , b , c

$Coefficient \:of \sf x^2(a) = 1$

$Coefficient \:of\: x (b) = 5$

$Constant\: term (c) = 5$

• putting values in formulae

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

$\sf x= \dfrac{-5\pm \sqrt{(5)^2-4\times 1\times 5}}{2\times 1}$

$\sf x= \dfrac{-5 \pm \sqrt{25-20}}{2}$

$\sf x= \dfrac{-5\pm \sqrt{5}}{2}$

$\sf x = \dfrac{-5-\sqrt{5}}{2} \ \ or \ \dfrac{-5+\sqrt{5}}{2}$

• roots of the equation

${\boxed{\sf{ \dfrac{-5-\sqrt{5}}{2}}}}$

${\boxed{\sf{ \dfrac{-5+\sqrt{5}}{2}}}}$

_________________________❤