Chapter 9.3, Problem 1E

To determine

The sign of the discriminant to predict the nature of equation $3x^2+4x-7=0$.

Introduction: The standard expression of the quadratic equation is $a{x}^2+bx+c=0$. The value of the disciminant of the quadratic equation is,

$b^2-4ac$

If the disciminant is negative number, then the roots of the equation are not real numbers and there is no real solution of the equation.

If the discriminant is positive then two condition are possible,

If $b^2-4ac$ is a perfect square, the two real number solutions are rational numbers,

If $b^2-4ac$ is not a perfect square, the two real number solutions are irrational,

If the discriminant is equal to $0$, there is one real number solution to the equation.