# How do you find the discriminant for x^2-9x+21=0 and determine the number and type of solutions?

Apr 16, 2018

color(crimson)("Discriminant " < 0, " given equation has " color(brown)("NO REAL ROOTS"

Both the roots are Imaginary

#### Explanation:

color(crimson)("Discriminant " < 0, " given equation has " color(brown)("NO REAL ROOTS"

Standard form of quadratic equation is $a {x}^{2} + b x + c = 0$

${x}^{2} - 9 x + 21$

$a = 1 , b = - 9 , c = 21 , D = {b}^{2} - 4 a c = {\left(- 9\right)}^{2} - \left(4 \cdot 1 \cdot 21\right) = - 3$

Since color(crimson)("Discriminant " < 0, " given equation has " color(brown)("NO REAL ROOTS"

Both the roots are Imaginary