Math, asked by ashishhirgond292, 9 months ago

2x^ -4x=-3 find the nature of root

Answers

Answered by AlluringNightingale
2

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

Since the discriminant of the given quadratic equation is less than zero , thus its roots are imaginary .

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