Determine the nature
of the roots 2x^ 2- 3x =4
Answers
Nature of roots : Real and distinct
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 .
Solution:
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 .
Answer:
REAL AND DISTINCT
Step-by-step explanation:
Nature of roots : Real and distinct
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 .
Solution:
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 .