find the discrimination of the equation 3x²-2x+1/3=0 and hence find the nature of its roots. Find them, if they are real.
Answers
Step-by-step explanation:
Given :-
3x²-2x+1/3=0
To find :-
Find the discrimination of the equation 3x²-2x+1/3=0 and hence find the nature of its roots. Find them, if they are real ?
Solution :-
Given quadratic equation is 3x²-2x+1/3=0
On comparing with the standard quadratic equation ax²+bx+c then
a = 3
b = -2
c = 1/3
The discriminant of ax²+bx+c = 0 is D = b²-4ac
=> D = (-2)²-4(3)(1/3)
=> D = 4-4
=> D = 0
We
know that
If the discriminant is zero then the roots are real and equal.
So, Given roots are real and equal.
We know that
quadratic formula X = [-b±√(b²-4ac)]/2a
Since, We have D = 0
So ,X = -b/2a
=> X = -(-2)/(2×3)
=> X = 2/6
=> X = 1/3
The roots are 1/3 and 1/3
Answer :-
Nature of the roots : Real and equal.
Roots : 1/3 and 1/3
Check:-
Given equation is 3x²-2x+1/3 = 0
=> (9x²-6x+1)/3 = 0
=> 9x²-6x+1 = 0×3
=> 9x²-6x+1 = 0
=> 9x²-3x-3x+1 = 0
=> 3x(3x-1)-1(3x-1) = 0
=> (3x-1)(3x-1) = 0
=> 3x-1 = 0
=> 3x = 1
=> x = 1/3
Roots are 1/3 and 1/3
Used formulae:-
→ The standard quadratic equation is
ax²+bx+c = 0
→The discriminant of ax²+bx+c = 0 is D = b²-4ac
→ If D = b²-4ac = 0 then the roots are real and equal.
→ quadratic formula X = [-b±√(b²-4ac)]/2a
Points to know:-
The discriminant of ax²+bx+c = 0 is
D = b²-4ac
→ If D > 0 then the roots are distinct and real
→ If D = 0 then the roots are real and equal.
→ If D > 0 then no real roots i.e. imaginary.
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