Question

Q.13 The product of two zeros of the polynomial f(x) = 2x 3 + 6x 2 -4x + 9
is 3, then find its third zero.

Answer 1

Answer:

Given:

Polynomial equation, f(x) = 2x³ +6x² -4x+9

Product of 2 zeroes = pq = 3

To find:

Third zero of the equation = r =?

Solution:

Condition to find zeros of polynomial, f(x) = 0.

f(x) = 2x³ +6x² -4x+9 = 0

Comparing the above equation with ax³ +bx² +cx+d = 0, we get,

a = 2, b = 6, c = -4, d = 9

Now,

pqr = -d/a

3r = -9/2

r = -9/6 = -3/2

r = -1.5

Third zero of the equation = r = -1.5

Answer 2

f(x)= 2x

3

+ 6x

2

− 4x+ 9

Let three zeroes be α,β,γ

Product of 3 zeroes

=

a

−d

=

2

−9

Given Product of 2 zeroes

=

3

or

α.β=

3

⇒ αβγ=

2

−9

⇒ 3γ=

2

−9

⇒ γ=

2

−3

Third zero is

2

−3

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