Question

if a, b,y are the zeroes of the polynomial f(x) = ax3 + bx2 + cx + d. Then find the value of
1/a,1/b,1/y=?

choose the correct option: a). -b/d. b)c/d. c)-c/a. d)-c/d
good luck
​

Answer 1

$\underline{\large{\sf\ \ \maltese\ Option (d)\ is\ correct\ option }}\\ \\ \ \therefore\ \dfrac{-c}{d}\\ \\ \sf\ Solution\ Refer\ to\ attachment !$

Answer 2

${\large{\bold{\rm{\underline{Question}}}}}\; \; \; \red \bigstar$

If α, β and γ are the zeros of the polynomial f(x) = ax³ + bx² + cx + d then ${\sf{\dfrac{1}{\alpha} + \dfrac{1}{\beta} + \dfrac{1}{\gamma}}}$ = ?

${\large{\bold{\rm{\underline{Given \; that}}}}}\; \; \; \red \bigstar$

α, β and γ are the zeros of the polynomial f(x) = ax³ + bx² + cx + d.

${\large{\bold{\rm{\underline{To \; find}}}}}\; \; \; \red \bigstar$

${\sf{\dfrac{1}{\alpha} + \dfrac{1}{\beta} + \dfrac{1}{\gamma}}}$ = ? (according to the above information)

${\large{\bold{\rm{\underline{Solution}}}}}\; \; \; \red \bigstar$

${\sf{\dfrac{1}{\alpha} + \dfrac{1}{\beta} + \dfrac{1}{\gamma}}}$ = -c/d

${\large{\bold{\rm{\underline{Full \; Solution}}}}}\; \; \; \red \bigstar$

➨ α + β + γ = -b/a

➨ αβ + βγ + γα = c/a

➨ αβγ = -d/a

➨ 1/α + 1/β + 1/γ

➨ βγ + αγ + αβ / αβγ

➨ c/a / -d/a

➨ -c/d

${\frak{Henceforth, \: -c/d \: is \: the \: value \: of \: \dfrac{1}{\alpha} + \dfrac{1}{\beta} + \dfrac{1}{\gamma}}}$

${\large{\bold{\rm{\underline{Additional \; information}}}}}\; \; \; \red \bigstar$

Knowledge about Quadratic equations -

★ Sum of zeros of any quadratic equation is given by ➝ α+β = -b/a

★ Product of zeros of any quadratic equation is given by ➝ αβ = c/a

★ A quadratic equation have 2 roots

★ ax² + bx + c = 0 is the general form of quadratic equation