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

Discriminant is 36.

x²-4x-5 = 0 have two real solutions.

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.

Answer 2

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.