Question

the nature of roots of the quadratic equation 2x^2-4x+3 = 0 is _______ real roots​

Answer 1

$\bf{ \underline{Answer:}}$

→ The nature of quadratic equation is no real roots.

$\bf{ \underline{Explanation :}}$

Given :

→ Quadratic equation :

$\tt{2x^2-4x+3={02x}^{2} − 4x+3=0}$

To find :

→ Nature of the roots of quadratic equation?

Solution :

→ To determine the nature we find discriminant,

$\tt{D=b^2-4acD={b}^{2} </p><p> − \: 4ac}$

1) If D<0, no real roots.

2) If D=0, two equal real roots.

3) If D>0, two distinct real roots.

→ Now, we find discriminant.

$\tt{2x^2-4x+3={02x}^{2} </p><p> −4x+3=0</p><p>}$

→ Here,

→ a=2

→ b=-4

→ c=3

$\tt{D=(-4)^2-4(2)(3)}$

$\tt{D={(−4)}^{2} </p><p> −4(2)(3)</p><p>}$

$\tt{D=16-24D=16−24}$

$\tt{D=-8D=−8}$

→ So,

→ D < 0 there is no real roots.

→ Therefore,

→ The nature of quadratic equation is no real roots.