Question

Find the discriminant for x 2 -4x+3=0. Hence find the nature of roots and find them if real.

Answer 1

Given polynomial :-

x² - 4x + 3 = 0

We know,

$\boxed{\bf{Discriminant,\ D=b^2-4ac}}$

In the given polynomial,

• a = 1
• b = -4
• c = 3

Putting the values →

$\longmapsto$ D = (-4)² - 4 × 1 × 3

$\longmapsto$ D = 16 - 12

$\longmapsto$ D = 4

As D > 0, so the roots are real and distinct.

____________________

► x² - 4x + 3 = 0

$\longmapsto$ x² - 3x - x + 3 = 0

$\longmapsto$ x(x - 3) - 1(x - 3) = 0

$\longmapsto$ (x - 3)(x - 1) = 0

$\longmapsto$ (x - 3) = 0  OR  (x - 1) = 0

$\longmapsto$ x = 3 OR  x = 1

Therefore, the roots of the given quadratic equation are 1 and 3.

Answer 2

Step-by-step explanation:

x² - 4x + 3 = 0

We know,

\boxed{\bf{Discriminant,\ D=b^2-4ac}}

Discriminant, D=b

2

−4ac

In the given polynomial,

a = 1

b = -4

c = 3

Putting the values →

\longmapsto⟼ D = (-4)² - 4 × 1 × 3

\longmapsto⟼ D = 16 - 12

\longmapsto⟼ D = 4

As D > 0, so the roots are real and distinct.

____________________

► x² - 4x + 3 = 0

\longmapsto⟼ x² - 3x - x + 3 = 0

\longmapsto⟼ x(x - 3) - 1(x - 3) = 0

\longmapsto⟼ (x - 3)(x - 1) = 0

\longmapsto⟼ (x - 3) = 0 OR (x - 1) = 0

\longmapsto⟼ x = 3 OR x = 1

Therefore, the roots of the given quadratic equation are 1 and 3.