Question

prove that

if ax2 + bx + c =0

x = + - b + root b2 -4ac /2a​

Answer 1

Answer:

ax

2

+bx+c=0 have real roots of opposite sign in (−2,2)

⇒x

2

+

a

b

x+

a

c

=0

(1) D≥0⇒

a

2

b

2

−

a

4c

≥0

(2) f(−2)>0⇒4−

a

2b

+

a

c

>0⇒1+

4a

c

−

2a

b

>0

(3) f(2)>0⇒4+

a

2b

+

a

c

>0⇒1+

4a

c

+

2a

b

>0

(4) αβ=−4<

a

c

<0⇒1+

4a

c

>0

(5) −2<−

2a

b

<2

Combining above conditions,

⇒1+

4a

c

−

∣

∣

∣

∣

∣

2a

b

∣

∣

∣

∣

∣

>0

∴(0,∞)

hope it will help you dear ❤️☺️☺️

Answer 2

Answer:

b^2/4a

Step-by-step explanation:

d=b^2-4ac=0

b^2=4ac

c=b^2/ 4a