Question

When D = +ve Then roots are *


ok​

Answer 1

Answer:

ax

2

+bx+c=0

The roots of the above equation are given by the quadratic formula

x=

2a

−b±

b

2

−4ac

Case I

b

2

−4ac<0

Then x=

2a

−b±i

∣b

2

−4ac∣

Hence the roots have negative real parts, since b>0.

For example, x

2

+2x+2=0 be any quadratic equation

⟹a=1,b=2,c=2

Now, b

2

−4ac=4−8<0

x=

2

−2±

−4

=−1±i

So, real part is negative.

Case II

b

2

−4ac=0

Then the roots are equal and negative.

For example, x

2

+2x+1=0 be any quadratic equation

⟹a=1,b=2,c=1

Now, b

2

−4ac=4−4=0

x=

2

−2±0

=−1

So, roots are equal and negative.

Case III

b

2

−4ac>0

(A)

b

2

−4ac

<b

For example, x

2

+3x+1=0 be any quadratic equation

⟹a=1,b=3,c=1

Now, b

2

−4ac=9−4=5>0

x=

2

−3±

5

5

<3=b

Thus, the roots are negative.

(B) If

b

2

−4ac

>b⟹−b+

b

2

−4ac>0

and −b−

b

2

−4ac

<0

Then we get one positive and one negative roots.

Step-by-step explanation:

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