discuss the nature of roots of the equation 2X2+X-3=0
Answers
Given :-
♦ The Quadratic equation is 2x²+x-3 = 0
To find :-
♦ The nature of the roots of the equation.
Solution :-
Given Quadratic equation is 2x²+x-3 = 0
On comparing with the standard quadratic equation ax²+bx+c = 0
• a = 2
• b = 1
• c = -3
To know the nature of the roots of the equation then we have to find the value of the discriminant of the equation.
We know that
The discriminant of the equation ax²+bx+c = 0 is D = b²-4ac
The Value of the discriminant of the given equation = D = (1)²-4(2)(-3)
=> D = 1-(-24)
=> D = 1+24
=> D = 25 > 0
The value of the discriminant is greater than zero
Nature of the roots :
The roots are distinct and real .
Answer :-
♦ The Quadratic equation is 2x²+x-3 = 0 has two distinct and real roots.
Used formulae:-
★ The discriminant of the equation ax²+bx+c = 0 is D = b²-4ac
Points to know:-
★If D > 0 then the equation has two distinct and real roots.
★If D = 0 then the equation has two equal and real roots.
★ If D < 0 then the equation has no real roots.