The quadratic polynomial P(x)=ax^2+bx+c has two different zeroes including -2. The quadratic polnomial Q(x)=ax^2+cx+b has two different zeroes including 3. If α and β be the other zeroes of P(x) and Q(x) respectively, then find the value of α/β

Open in App

Solution

Dear student
$G i v e n : Q u a d r a t i c p o l y n o m i a l a r e p (x) = a x^{2} + b x + c a n d q (x) = a x^{2} + c x + b T h e r o o t s o f p (x) a r e - 2 a n d α w h e r e a s t h e r o o t s o f q (x) a r e 3 a n d β . T a k i n g p (x) = a x^{2} + b x + c, w e g e t P r o d u c t o f r o o t s = - 2 \times α = \frac{c}{a} \Rightarrow α = \frac{- c}{2 a} . . . (1) S i m i l a r l y, o n t a k i n g q (x) = a x^{2} + c x + b, w e g e t P r o d u c t o f r o o t s = 3 \times β = \frac{b}{a} \Rightarrow β = \frac{b}{3 a} . . . (2) O n d i v i d i n g (1) b y (2), w e g e t \frac{α}{β} = \frac{\frac{- c}{2 a}}{\frac{b}{3 a}} = \frac{- c}{2 a} \times \frac{3 a}{b} = \frac{- 3 c}{2 b}$
Regards

Suggest Corrections

Similar questions

p (x) = a x^{2} + b x + c, α + β = 2

α β = - 8

α, β

p (x)

∴

a, b

c

α

β

p (x) = a x^{2} + b x + c, (a \neq 0)

α . β =

α, β

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

\frac{α^{2}}{β} + \frac{β^{2}}{α} =

α

β

P (x) = a x^{2} + b x + c, \frac{1}{α} + \frac{1}{β} =

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

α & β,

\frac{1}{α} + \frac{1}{β} .

Join BYJU'S Learning Program