if 2x^2-3x-4=0 then what is the nature of the roots of quadratic equation?
Answers
Answer:
Nature of Roots : Real and distinct
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Step-By-Step Explanation :
Note:
★ The possible values of the the variable which satisfy the equation are called its roots or solutions .
★ The discriminant of the quadratic equation
ax² + bx + c is given by ⇒ D = b² - 4ac .
★ If D > 0 , then the roots are real and distinct .
★ If D = 0 , then the roots are real and equal .
★ If D < 0 , then the roots are imaginary .
The given quadratic equation is ;
2x² + 3x - 4 = 0
Comparing with the general form of the quadratic equation ax² + bx + c = 0 , we have ;
a = 2 , b = 3 , c = -4
Now,
The discriminant of the given quadratic equation will be given as ;
=> D = b² - 4ac
=> D = 3² - 4×2×(-4)
=> D = 9 + 32
=> D = 41
=> D > 0
Clearly,
The discriminant of the given quadratic equation is greater than zero .
Thus,
Its roots will be Real and Distinct.