# Discriminant of the following quadratic equation is: $2{x^2} - 5x + 3 = 0$

Answer

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Hint: We solve this problem by using the formula for finding the discriminant of

quadratic equations.

The given quadratic equation is $2{x^2} - 5x + 3 = 0$

Comparing the given equation with$a{x^2} + bx + c = 0$, we get $a = 2,b = - 5,c = 3$

Formula for finding the discriminant of quadratic equation$D = {b^2} - 4ac$$ \to (1)$

Substituting a, b and c values in equation (1)

$ \Rightarrow D = {( - 5)^2} - 4(2)(3)$

$D = 25 - 24 = 1$

$\therefore $Discriminant of the given quadratic equation $2{x^2} - 5x + 3 = 0$ is 1.

Note: General form of quadratic equation is$a{x^2} + bx + c = 0$. Discriminant of any quadratic equation is $D = {b^2} - 4ac$. The discriminant tells us whether there are two

solutions, one solution or no solution for the given quadratic equation. If D>0, then the

equation has two real solutions. If D=0, then there are no solutions for the equation. If D<0,

then there is one solution. Here in our case we got Discriminant value as 1. So the given

quadratic equation has two real solutions (two real roots).

quadratic equations.

The given quadratic equation is $2{x^2} - 5x + 3 = 0$

Comparing the given equation with$a{x^2} + bx + c = 0$, we get $a = 2,b = - 5,c = 3$

Formula for finding the discriminant of quadratic equation$D = {b^2} - 4ac$$ \to (1)$

Substituting a, b and c values in equation (1)

$ \Rightarrow D = {( - 5)^2} - 4(2)(3)$

$D = 25 - 24 = 1$

$\therefore $Discriminant of the given quadratic equation $2{x^2} - 5x + 3 = 0$ is 1.

Note: General form of quadratic equation is$a{x^2} + bx + c = 0$. Discriminant of any quadratic equation is $D = {b^2} - 4ac$. The discriminant tells us whether there are two

solutions, one solution or no solution for the given quadratic equation. If D>0, then the

equation has two real solutions. If D=0, then there are no solutions for the equation. If D<0,

then there is one solution. Here in our case we got Discriminant value as 1. So the given

quadratic equation has two real solutions (two real roots).

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