Find discrimant of 3x^2-9x+20

A quadratic equation is written in the form a x 2 + b x + c = 0 Always change to this form first The discriminant is Δ = b 2 − 4 a c The solutions to an equation are called the 'roots' and are referred to as α and β The value of Δ tells us about the nature of the roots. If Δ > 0 ⇒ the roots are real and unequal (2 distinct roots) If Δ > 0 and a prefect square ⇒ the roots are real, unequal and ... ... ... ... ... ... ... ... ... ... ... . ... ... ... ... ... . . rational If Δ = 0 ⇒ the roots are real and equal (1 root) If Δ < 0 ⇒ the roots are imaginary and unequal Note that if a or b are irrational, the roots will be irrational. − 3 x 2 + 9 x = 4 ⇒ 3 x 2 − 9 x + 4 = 0 Δ = b 2 − 4 a c Δ = ( − 9 ) 2 − 4 ( 3 ) ( 4 ) = 33 33 > 0 and is not a perfect square Therefore, there are two roots which will be real and unequal.

-159 by b² - 4ac