Chapter 1, Problem 4VE

Solution

To write: The quadratic equation which has a negative discriminant.

The required quadratic equation is $8x^2+5x+1=0$ where $a\ne 0$ .

Given:

The discriminant $\left(D\right)$ of the quadratic equation is negative.

Concept used:

Any quadratic equation of the form $a{x}^2+bx+c=0\text{ where }a\ne 0$ has the discriminant $D=b^2-4ac$ .

Calculation:

Consider the quadratic equation in standard form is $a{x}^2+bx+c=0\text{ where }a\ne 0$ . Since, the discriminant of it is negative. Therefore,

  $b^2-4ac<0$

Now, consider the parameters $a,b\text{and }c$ such that $b^2-4ac<0$ . Now, many more combinations of $a,b\text{and }c$ can be obtained, Therefore, by hit and trial method one such combination is evaluated as ${\left(5\right)}^2-4\left(8\right)\left(1\right)<0$ .

Comparing ${\left(5\right)}^2-4\left(8\right)\left(1\right)<0$ with $b^2-4ac<0$ gives, $b=5,a=8\text{ and }c=1$ .

Hence, the required quadratic equation is written as $8x^2+5x+1=0$ where $a\ne 0$ .