Question

Given that one of the cubic polynomial ax³+bx²+cx+d is zero, then find the product of the other two zeros...
please helppppp mere.....

Answer 1

Hey!

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Given,

p ( x ) = ax³+bx²+cx+d = 0

Let one zero be = @ (alpha)
Let second zero be = ß (beta)
Let third zero be = γ (gamma)

Where @ = 0

We know,


Sum of two zeroes at a time = - b/a

@ß + ßγ + γ@ = c/a

@ = 0

0 × ß + ßγ + γ × 0 = c/a

ßγ = c/a

Thus, Product of other two zeroes = c/a


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Hope it helps...!!!

Answer 2

Heya !!

Here's your answer.. ⬇⬇
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➡ Given :- ax³+bx²+cx+d is an cubic polynomial.
p( x ) = ax³+bx²+cx+d
One zero of p(x) = 0

➡ To Find :- Product of other two zeros.

➡ Solution :- Let the three zeros be
$\alpha \: \: \beta \: \: and \: \: \gamma \\ \\ given \: \: that \: \: one \: \: zero \: \: = 0 \\ \\ \alpha = 0 \\ \\ sum \: \: of \: \:product \: \: of \: \: two \: \: zeroes \: = \frac{c}{a} \\ \\ \alpha \beta + \beta \gamma + \gamma \alpha = \frac{c}{a} \\ \\ (0) \beta + \beta \gamma + \gamma (0) = \frac{c}{a} \\ \\ 0 + \beta \gamma + 0 = \frac{c}{a} \\ \\ \beta \gamma = \frac{c}{a} \\ \\ product \: \: of \: \: two \: \: zeros \: = \frac{c}{a}$
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Hope it helps..

Thanks :))