Question

25. Find the discriminant of the quadratic equation 2x^2-4x+3=0, and
hence find the nature of its roots.​

Answer 1

Answer:-

Discriminant (d) = -8

Step - by - step explanation:-

Formula used :-

We know that,

$\bf{discriminant \: = {b}^{2} - 4ac}$

Solution :-

According to the question,

Given equation is

$\implies \: 2 {x}^{2} - 4x + 3 = 0 \: \: ......(1)$

Now ,

Standard equation is

$\bf{ \implies \: a {x}^{2} + bx + c} \: .....(2)$

Comparing the equation (1) and (2)

We get,

• a = 2
• b = -4
• c= 3

Hence,

$\bf{discriminant \: (d) = {b}^{2} - 4ac} \\ \\ \bf{ \implies \: d = {( - 4)}^{2} - 4 \times 2 \times 3} \\ \\ \implies \: \bf{ d \: = 16 - 24} \\ \\ \implies \: \boxed{\bf{ d = - 8}}$

For nature of roots,

We know that,

if,

• d <0 (roots are Imaginary)
• d >0 (roots are real)

because( -8< 0)

Hence, The nature of roots of this given equation is imaginary.