2x^ -4x=-3 find the nature of root
Answers
Answer :
Imaginary
Note:
★ The possible values of the variable which satisfy the equation are called its roots or solutions .
★ A quadratic equation can have atmost two roots .
★ The general form of a quadratic equation is given as ; ax² + bx + c = 0
★ If α and ß are the roots of the quadratic equation ax² + bx + c = 0 , then ;
• Sum of roots , (α + ß) = -b/a
• Product of roots , (αß) = c/a
★ If α and ß are the roots of a quadratic equation , then that quadratic equation is given as : k•[ x² - (α + ß)x + αß ] = 0 , k ≠ 0.
★ The discriminant , D of the quadratic equation ax² + bx + c = 0 is given by ;
D = b² - 4ac
★ If D = 0 , then the roots are real and equal .
★ If D > 0 , then the roots are real and distinct .
★ If D < 0 , then the roots are unreal (imaginary) .
Solution :
Here ,
The given quadratic equation is ;
2x² - 4x = -3
The given quadratic equation can be rewritten as ; 2x² - 4x + 3 = 0
Comparing the given quadratic equation with the general quadratic equation ax² + bx + c = 0 ,
We have ;
a = 2
b = -4
c = 3
Now ,
The discriminant of the given quadratic equation will be ;
=> D = b² - 4ac
=> D = (-4)² - 4•2•3
=> D = 16 - 24
=> D = - 8
=> D < 0