Question

What is the discriminant of $9{{x}^{2}}+2=10x$?

Answer 1

The expression ${{b}^{2}}-4ac$ is the part of the quadratic formula and is known as the discriminant of the quadratic equation. First we will convert the given equation into standard form $a{{x}^{2}}+bx+c=0$. Then by substituting the values of a, b and c in the formula and simplifying the obtained equation we will get the desired answer.

Complete step by step solution:
We have been given an equation $9{{x}^{2}}+2=10x$.
We have to find the discriminant of the given equation.
We know that discriminant is the part of a quadratic formula and is given by $D={{b}^{2}}-4ac$.
Now, let us first convert the given equation in to general form then we will get
$\Rightarrow 9{{x}^{2}}-10x+2=0$
Then by comparing the above obtained equation with the standard equation $a{{x}^{2}}+bx+c=0$ we will get
$\Rightarrow a=9,b=-10,c=2$
Now, substituting the values in the discriminant formula we will get
$\Rightarrow D={{\left( -10 \right)}^{2}}-4\times 9\times 2$
Now, simplifying the above obtained equation we will get
$\begin{aligned} & \Rightarrow D=100-72 \\\ & \Rightarrow D=28 \\\ \end{aligned}$
Hence we get the value of discriminant as 28 for the given equation.

Note: By evaluating the value of discriminate we can identify the nature of roots a quadratic equation has. If the value of discriminant is zero then the equation has only one solution, for the equation has two roots the value of discriminant must be greater than one. We can find the values of roots of the equation by using the quadratic formula.