Shortcut Methods

CBSE Class 11 and Class 12 Exams#

Coefficient of x^2 = 3 Coefficient of x = -2 Constant term = 5 Discriminant D>0 (Since roots are real)

The quadratic equation is $$3x^2-2x+5=0$$

As per hit-and-trial method, the values of a, b, and c are determined as $$a=3, \ b=-2, \ and \ c=5$$ So, we can write it as $$3x^2-3x+x+5=0$$ $$3x(x-1)+(x+5)=0$$ Taking 3x common from the first two terms, and 1 common from the last two terms, we get $$3x(x-1)+1(x+5)=0$$ $$(x+5)(3x-1)=0$$ $$\therefore x=\frac{-5}{3}, and \ \frac{1}{3}$$ Hence, the roots are -5/3 and 1/3 which are real and distinct.