Question

if one of the zero of the cubic polynomial ax cube + 2 X square +cx + D is zero then the product of theother two zero is

Answer 1

Heya ur answer_-_-_-_

(a) Let p(x) = x3 + ax2 + bx + c
Let a, p and y be the zeroes of the given cubic polynomial p(x).
∴  α = -1                                        [given]
and p(−1) = 0
⇒ (-1)3 + a(-1)2 + b(-1) + c = 0
⇒ -1 + a- b + c = 0
⇒ c = 1 -a + b                                                             …(i)
We know that,
βγ = 1 -a + b                                                                [from Eq. (i)]
Hence, product of the other two roots is 1 -a + b.

αβγ = -c
⇒ (-1)βγ = −c                                                                             [∴α = -1]
⇒ βγ = c

Hope it helps u

Answer 2

Method of Solution :

In this question , it is given that one of the zero of the Cubic Polynomial ax³ + 2x² + cx + d is 0



Let a, 0,0 be the Zeroes of ax³ + 2x² + cx + d.

Then, Sum of the products of Zeroes!

Note : ab+ba+ac = c/a

Now, Substitute this on Equation!

Sum of Zeroes of Cubic Polynomial= ab+ba+ac = c/a

✒ab + b×0 + a×0 = c/a

✒ ab + 0 + 0 = c/a

✒ ab = c/a

[ Note: a = alpha and b = beta! ]


Hence, Required other product of Zeroes is c/a.