Question

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

Answer 1

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).