Question

Write the discriminant of $17x^2+21x-3=0$ and determine the nature of its root.

Answer 1

Step 1: Comparison with the standard form of quadratic equation $a{x}^2+bx+c=0$

The given quadratic equation is $17x^2+21x-3=0$.

Here, $a=17,b=21$ and $c=-3$.

Step 2: Finding the discriminant

Using the formula for discriminant $\left(D\right)=b^2-4ac$ and substituting the values of $a,b$ and $c$ we get

$\begin{array}{rcl}D& =& {\left(21\right)}^2-4\left(17\right)(-3)\\ & =& {\left(21\right)}^2+204\\ & =& 441+204\\ & =& 645\end{array}$

Step 3: Determining the nature of the roots of the equation

We know that the value of the discriminant decides the nature of the roots of the quadratic equation.

If $D>0$, then the quadratic equation has real and unequal roots.

If $D=0$, then the quadratic equation has real and equal roots.

If $D<0$, then the quadratic equation has no real roots.

For the given quadratic equation, $D>0$. So, the equation has real and unequal roots.

Therefore, the quadratic equation $17x^2+21x-3=0$ has real and unequal roots.