# 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).

Last updated date: 18th Sep 2023

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