Question

The nature of roots of quadratic equation x square -8x+12=0

Answer 1

Given :-

Quadratic equation:- x² -8x + 12

To find :-

Nature of roots

Solution:-

We can find the nature of roots by the discriminant of Quadratic equation that is b²-4ac . It is represented by D We have some cases to know the nature .

D >0 Roots are real and distinct

D<0 Roots are complex and conjugate

D=0 Roots are equal and real

So, firstly lets find discriminant

x² -8x + 12 = 0

• a = 1
• b = -8
• c = 12

By compared with ax² + bx + c = 0

D = b²-4ac

D = (-8)² -4(1)(12)

D = 64 -48

D = 16

So, Discriminant is 16 i.e D>0 So, roots are real and distinct

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Alternate method:-

Firstly we find the roots of the Quadratic equation

x² -8x + 12 = 0

By splitting the midlle term

x² -2x -6x + 12 = 0

x(x-2) -6(x-2) = 0

(x-2)(x-6) = 0

x-2 = 0 and x-6 = 0

x = 2 , 6

Now we got the roots that are 2, 6 i.e those are real and distinct

So, the nature of roots of given Quadratic equation is real and distinct