How do you find the value of the discriminant and state the type of solutions given #9n^2-3n-8=-10#?

1 Answer
Aug 8, 2016

Answer:

#Delta=-63#
roots are not real.

Explanation:

The #color(blue)"discriminant"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(Delta=b^2-4ac)color(white)(a/a)|)))#
where a, b and c are the coefficients in the standard quadratic equation. The value of the discriminant provides information on the nature of the roots.

#color(orange)"Reminder" color(red)(|bar(ul(color(white)(a/a)color(black)(ax^2+bx+c=0)color(white)(a/a)|)))#

#•b^2-4ac>0tocolor(blue)"roots are real and irrational"#

#•b^2-4ac>0" and a square"tocolor(blue)"roots are real and rational"#

#•b^2-4ac=0tocolor(blue)"roots are real/rational and equal"#

#•b^2-4ac<0tocolor(blue)"roots are not real"#

Equate the given equation to zero.

#rArr9n^2-3n+2=0#

here a = 9 ,b =- 3 and c=2

#rArrb^2-4ac=(-3)^2-(4xx9xx2)=-63<0#

Since discriminant is less than zero then roots of the quadratic equation are not real.

Solving the equation using the #color(red)"quadratic formula"#

#x=(3±sqrt(-63))/18=3/18±(3isqrt7)/18=1/6+-1/6isqrt7#

The roots of the equation are not real. They are complex.