You visited us 2 times! Enjoying our articles? Unlock Full Access!

Algebra of Limits

If α, β are t...

Question

If $α, β$ are the roots of $a x^{2} + b x + c = 0$ , the correct statements about the equation a ${(x - 2)}^{2}$ + b(x - 2) + c = 0 is

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B

$α, β$ are the roots of a $x^{2}$ + bx + c = 0

$\Rightarrow a α^{2} + b α + c = 0 a n d a β^{2} + b β + c = 0$ clearly, if we substitute $α$ + 2

and $β$ + 2 in a ${(x - 2)}^{2}$ + b(x - 2) + c, we get

$a (α + 2 - 2)^{2} + b (α + 2 - 2) + c = a α^{2} + b α + c$

= 0

$\Rightarrow α + 2 a n d β + 2$ are the roots.

Suggest Corrections

Similar questions

α

β

a x^{2} + b x + c = 0

c x^{2} + b x + a = 0

f (x + 2) = a x^{2} + b x + c = 0

α, β

α < - 2 < β

f (x) = A x^{2} + B x + C

α, β

a x^{2} + b x + c = 0, a < 0

k

k > α > β

f (x) = a x^{2} + b x + c

α, β

a x^{2} + b x + c = 0

a (x - 2)^{2} - b (x - 2) (x - 3) + c (x - 3)^{2} = 0

a \neq 0

α, β

a x^{2} + b x + c = 0

2 + α, 2 + β

Join BYJU'S Learning Program