Question

Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the solutions are real or imaginary.

x^2 - 4x - 5 = 0

Answer 1

ANSWER

$\boxed {2 \: \: distinct \: \: real \: \: roots}$


EXPLANATION


The given equation is

${x}^{2} - 4x - 5 = 0$

By comparing to

$a {x}^{2} + bx + c = 0$

$a=1,b=-4,c=-5$


The discriminant is given by;


$D = {b}^{2} - 4ac$


$D = {( - 4)}^{2} - 4(1)( - 5)$


$D = 16 + 20$



$D = 36$
The discriminant is 36.


Since 36 is greater than zero, the given quadratic equation will have two distinct real roots.

Answer 2

Answer:

Discriminant is 36.

x²-4x-5 =  0 have two real solutions.

Step-by-step explanation:

Given equation is :

x²-4x-5=  0

we have to find discriminant of above equation.

general quadratic equation is :

ax²+bx+c =  0

comparing general equation with quadratic equation,we get

a =  1 ,b=  -4 and c =  -5

The formula to find discriminant is :

D =  b²-4ac

putting the values of a,b and c in formula to find discriminant,we get

D =  (-4)²-4(1)(-5)

D  =  16+20

D =  36 > 0

if an equation has Discriminant real and perfect square ,there are exactly two real solutions.

hence, 36 is real and greater than zero,so give equation have two real solution.