Question

The discriminant of quadratic equation
$x { }^{2} + 4x + 1 = 0$

(a) 12
(b) 14
(c) 16
(d) -12​

Answer 1

Given Equation

x² + 4x + 1 = 0

To Find

Discriminant

So Compare with

ax² + bx + c = 0

We get

a = 1 , b = 4 and c = 1

Formula

D = b² - 4ac

Now

D = (4)² - 4 × 1 × 1

D = 16 - 4

D = 12

Answer

D = 12 , Option (a) is correct

More Information

When D > 0

It is real and Distinct

When D = 0

It is equal and real roots

When D<0

No real roots

Answer 2

Answer:

Given :-

• A quadratic equation is x² + 4x + 1 = 0.

To Find :-

• What is discriminate.

Solution :-

$\longmapsto \sf {x}^{2} + 4x + 1 =\: 0$

By comparing the quadratic equation x² + 4x + 1 = 0 with the quadratic equation ax² + bx + c = 0 [ a ≠ 0] , we get :

• a = 1
• b = 4
• c = 1

Now,

$\mapsto$ The discriminate = 0

Then, b² - 4ac = 0

↦ $\sf Discriminate =\: {(4)}^{2} - 4 \times 1 \times 1$

↦ $\sf Discriminate =\: 4 \times 4 - 4$

↦ $\sf Discriminate =\: 16 - 4$

➲ $\sf\bold{\red{Discriminate =\: 12}}$

$\therefore$ The discriminate of the quadratic equation x² + 4x + 1 = 0 is 12 .

Hence, the correct options is option no (a) 12.

$\rule{300}{2}$

Extra Information :-

$\leadsto$ The general form of equation is ax² + bx + c.

[ If a = 0 then the equation becomes to a linear equation. If b = 0 then the roots of the quadratic equation becomes equal but opposite in sign. If c = 0 then one of the roots is zero. ]

$\leadsto$ b² = 4ac is the discriminate of the equation. There are two roots.

i) When b² - 4ac = 0, then roots are real & equal.

ii) When b² - 4ac > 0, then the roots are imaginary and unequal.

iii) When b² - 4ac < 0, then there will be no roots.