Question

Use the discriminant to determine the number and type of solutions the equation has. x^2 + 6x + 12 = 0

Answer 1

Answer :-

Equation has no real roots. Roots are imaginary.

Solution :-

x² + 6x + 12 = 0

Comparing with ax² + bx + c = 0 we get,

• a = 1
• b = 6
• c = 12

Discriminant = b² - 4ac

= 6² - 4( 1 )( 12 )

= 36 - 48

= - 12

Since, Discriminant < 0 the equation has no real roots and roots are imaginary

Learn more :

Nature of Roots

A quadratic equation ax² + bx + c = 0 (a ≠ 0)

Case 1 :

If b² - 4ac i.e discriminant > 0 the equation two distinct real roots.

Graph of the equation touches the X - axis at two points

Case 2:

If the discriminant b² - 4ac = 0 the equation has 2 eqal real roots.

Graph of the equation touches the X - axis only at one points

Case 3 :

If the discriminant b² - 4ac < 0 the equation has no real roots. Roots are imaginary.

Graph of the equation doesn't cut X - axis.

Answer 2

Answer:

Roots : Virtual and Imaginary

Step-by-step explanation:

p (x) = x^2 + 6x + 12

We know that,

D = b^2 - 4ac

D = 6^2 - 4×12×1

D = 36 - 48

D = -12

Here,

D < 0

Since, -12 < 0

So the roots are virtual and imaginary.