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