Question

Find the value of a for which the equation `(α-12)x^2+2(α-12)x+2=0` has equal roots.  

Answer 1

Given: 

`(α-12)x^2+2(α-12)x+2=0 ` 

Here, 

`a=(α=12),b=2(α-12) and c=2` 

It is given that the roots of the equation are equal; therefore, we have 

`D=0` 

⇒`(b^2-4ac)=0` 

⇒`{2(α-12)}^2-4xx(α-12)xx2=0` 

⇒`4(α^2-24α+144)-8a+96=0` 

⇒`4α^2-96α+576-8α+96=0` 

⇒`4α^2-104α+672=0` 

⇒`α^2-26α+168=0` 

⇒`α^2-14α-12α+168=0` 

⇒`α(α-14)-12(α-14)=0` 

⇒`(α-14)(α-12)=0` 

∴`α=14  or  α=12` 

If the value ofα is 12, the given equation becomes non-quadratic.
Therefore, the value of α will be 14 for the equation to have equal roots.