Question

If one zero pf the quadratic polynomial ax^2+bx+c is four times the other,then prove that 4b^2=25ac

Answer 1

4$b^{2}$ = 25ac, it is proved.

Step-by-step explanation:

Let α and 4α be the two zeros of the quadratic polynomial.

∴ α + 4α= 5α = $\frac{- b}{a}$

⇒ α = $\frac{- b}{5a}$     ... (1)

Also,

α·4α = $\frac{c}{a}$

⇒ 4$α^{2}$ =  $\frac{c}{a}$      ... (2)

Putting the value of Equn. (1) in (2), we get

4$[tex]\frac{- b}{5a}$^{2}[/tex] =  $\frac{c}{a}$  

⇒ $\frac{b^{2} }{25a^{2} }$ = $\frac{c}{4a}$  

⇒ 4$b^{2}$ = 25ac

Hence, it is proved.

Answer 2

Answer:

Step-by-step explanation:

Let α and 4α be the two zeros of the quadratic polynomial.

∴ α + 4α= 5α =

⇒ α =     ... (1)

Also,

α·4α =

⇒ 4 =        ... (2)

Putting the value of Equn. (1) in (2), we get

4^{2}[/tex] =    

⇒ =  

⇒ 4 = 25ac

Hence, it is proved.