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

2 thoughts on “find the discriminant of the equation 3×2-5x+2=0 and hence write the nature of roots”

1. Step-by-step explanation:

   given

   a = 3, b= – 5, c = 2

   discriminant = b² – 4ac

   = 3² – 4 ( -5 ) ( 2 )

   = 9 – ( – 40 )

   = 9 + 40

   = 49

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2. Discriminant

   Discriminant is denoted by ‘[tex]D[/tex]’ and given by:

   [tex]D = b^2 – 4ac[/tex]

   Nature of roots

   When we find the value of [tex]D[/tex], we can identify the nature of roots if:

   [tex]\bigstar[/tex] [tex]D[/tex] is greater than 0, roots are real and distinct.

   [tex]\bigstar[/tex] [tex]D = 0[/tex], roots are real and equal.

   [tex]\bigstar[/tex] [tex]D[/tex] is lesser than 0, roots are imaginary.

   Solution

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

   [tex]\Longrightarrow a = 3[/tex]

   [tex]\Longrightarrow b = -5[/tex]

   [tex]\Longrightarrow c = 2[/tex]

   Now, let us find the discriminant.

   [tex]\Longrightarrow D = b^2 – 4ac[/tex]

   [tex]\Longrightarrow D = (-5)^2 – (4 \times 3 \times 2)[/tex]

   [tex]\Longrightarrow D = 25 – 24[/tex]

   [tex]\Longrightarrow{\boxed{D = 1}}[/tex]

   Since Discriminant is greater than [tex]0[/tex], roots are real and distinct.

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