How do you describe the nature of the roots of the equation 7x^2=4x+1?

1 Answer
Aug 31, 2016

Roots are irrational. In the given equation these are
-2/7-sqrt11/7 and
-2/7+sqrt11/7

Explanation:

Nature of roots of an equation ax^2+bx+c=0/ are determined by its discriminant, which is b^2-4ac.

Assuming that the coefficients a, b and c are rational,

if discriminant is zero, there is one root and we also say roots coincide.

if discriminant is negative, roots are complex,

if discriminant is positive and square of a rational number, roots are rational

and if discriminant is positive but not a square of a rational number, roots are irrational.

As the equation 7x^2=4x+1
hArr7x^2-4x-1=0, the discriminant is (-4)^2-4×7×(-1)=16+28=44, which is positive but not a square of a rational number. Hence roots are irrational

In fact, according to quadratic formula roots are

((-4)+-sqrt44)/(2×7) or

-4/14+-2sqrt11/14 or

-2/7-sqrt11/7 and
-2/7+sqrt11/7