Question

Find the roots of each of the following quadratic equations if they exist by the method of completing the squares:
x2 + x + 3 = 0

Answer 1

Question:

Find the roots of the following quadratic equations, if they exist by the method of completing the square: x² + x + 3 = 0

Answer:

No real roots exists.

Note:

• The possible values of unknown (variable) for which the equation is satisfied are called its solutions or roots .

• If x = a is a solution of any equation in x , then it must satisfy the given equation otherwise it's not a solution (root) of the equation.

• The discriminant of the the quadratic equation

ax² + bx + c = 0 , is given as ; D = b² - 4ac

• If D > 0 then its roots are real and distinct.

• If D < 0 then its roots are imaginary.

• If D = 0 then its roots are real and equal.

Solution:

Here,

The given quadratic equation is :

x² + x + 3 = 0

Clearly, here we have ;

a = 1

b = 1

c = 3

Now,

The discriminant will be ;

=> D = b² - 4ac

=> D = 1² - 4•1•3

=> D = 1 - 12

=> D = - 11. ( D < 0 )

Since,

The discriminant of the given quadratic equation is less than zero , thus there exist no real roots.

Answer 2

$\huge{\boxed{\pink{ANSWER}}}$

Given,

$x^2+x+3=0$

To check whether roots exist ,

we need to calculate the discriminent value

D = $b^2-4ac$

From the given equation ,

• a = 1
• b = 1
• c = 3

D = 1 - 12

D = -11

D < 0, => No real roots