Question

Find the roots of the following quadratic equations (if they exist) by the method of completing the
square : x²+5x+7=0​

Answer 1

Answer:

no real roots

Step-by-step explanation:

x2 + 5x + 7 = 0

transfer 7 on other side

x2 + 5x = -7

divide x2 coefficient on both sides

x2 + 5x = -7

now add (5/2) square  on both sides

x2 + 5x + (5/2) square = -7 + (5/2) square

this can be written as (a + b)square form

then, (x+5/2) square = -7 + 25/4

(x + 5/2) square =( -28 + 25)/4

(x + 5/2) square = (-4/4)

(x + 5/2) square = -1 < 0

but (x + 5/2) square cannot be negative for real value of x. so, there is no real value satisfing the given equation. therefore the given equation has no real roots.