Question

find the discriminant of the equation 3x2-5x+2=0 and hence write the nature of roots

Answer 1

Step-by-step explanation:

given

a = 3, b= - 5, c = 2

discriminant = b² - 4ac

= 3² - 4 ( -5 ) ( 2 )

= 9 - ( - 40 )

= 9 + 40

= 49

Answer 2

Discriminant

Discriminant is denoted by '$D$' and given by:

$D = b^2 - 4ac$

Nature of roots

When we find the value of $D$, we can identify the nature of roots if:

$\bigstar$ $D$ is greater than 0, roots are real and distinct.

$\bigstar$ $D = 0$, roots are real and equal.

$\bigstar$ $D$ is lesser than 0, roots are imaginary.

Solution

We are given a quadratic equation $3x^2-5x+2=0$. Let us note the values of $a,b$ and $c$.

$\Longrightarrow a = 3$

$\Longrightarrow b = -5$

$\Longrightarrow c = 2$

Now, let us find the discriminant.

$\Longrightarrow D = b^2 - 4ac$

$\Longrightarrow D = (-5)^2 - (4 \times 3 \times 2)$

$\Longrightarrow D = 25 - 24$

$\Longrightarrow{\boxed{D = 1}}$

Since Discriminant is greater than $0$, roots are real and distinct.