Question

If α and β are zeroes of the polynomial f(x)=ax^2+bx+c then find the value of α/β+β/α​

Answer 1

Step-by-step explanation:

alpha+beta=-b/a

alpha*beta=c/a

alpha/beta+beta/alpha( taking lcm)

(alpha)²+(beta)²/apha*beta

(alpha+beta)²-2alpha*beta/alpha*beta

(-b/c)²- 2*c/a/c/a

Answer 2

SOLUTION :-

Since, α and β are zeroes of p (x) = ax² + bx + c,

.·. α + β = -b/a and αβ = c/a.

$\dfrac{\alpha}{\beta} + \dfrac{\beta}{\alpha} = \dfrac{{\alpha}^{2} + {\beta}^{2}}{\apha \beta}$

$\implies{\dfrac{{(\alpha + \beta)}^{2} - 2 \apha \beta}{\apha \beta}}$

$\implies{\dfrac{\dfrac{-b}{a}^{2} - 2 (\dfrac{c}{a})}{\dfrac{c}{a}}}$

$\implies{\dfrac{\dfrac{{b}^{2}}{{a}^{2}} - \dfrac{2c}{a}}{\dfrac{c}{a}}}$

$\implies{\dfrac{({b}^{2} - 2ac)}{{a}^{2}} \times \dfrac{a}{c} = \dfrac{{b}^{2} - 2ac}{ac}}$

So, the value of α/β + β/α is $\dfrac{{b}^{2} - 2ac}{ac}}$