Question

the product of two zeros of polynomial p(x) is - 3 the third zero os 11 p(x)=3x³+bx²-66x+d find the value of d​

Answer 1

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Answer 2

Given :- The product of two zeros of polynomial p(x) is (-3) and the third zero is 11 . p(x) = 3x³+bx²- 66x + d.

To Find :-

• value of d ?

Formula used :-

Consider the cubic polynomial P(x) =ax³ + bx² + cx + d = 0 ,a ≠ 0.

If α, β and γ are zeros of P(x),

Then :-

• Product of zeros = αβγ = (-d)/a .

Solution :-

Comparing the given polynomial p(x) = 3x³+bx²- 66x + d = 0, with P(x) =ax³ + bx² + cx + d = 0, we get ,

• a = 3
• b = b
• c = (-66)
• d = d .

Let us assume that, three zeros of the given Polynomial are α, β and γ .

Also, given that :-

• Product of two zeros = α * β = (-3) .
• Third zero = γ = 11 .

Therefore,

→ α * β * γ = (-3) * 11 = (-33). = Product of zeros.

Also,

→ Product of zeros = (-d)/a .

Putting all values Now, we get,

→ (-33) = (-d) / 3

→ (-33) * 3 = (-d)

→ (-99) = (-d)

→ (-1) * 99 = (-1) * d

→ d = 99 . (Ans.)

Hence, value of d will be 99.