Question

8.
If one zero of the polynomial 4x² – 8kx - 9 is negative of the other, find the value of k.​

Answer 1

Given :-

One zero of the polynomial 4x² – 8kx - 9 is negative of the other.

To find :-

Value of k.

Solution :-

General form of an equation is given as,

ax² + bx + c = 0

Where,

• Sum of zeroes = -b/a
• Product of zeroes = c/a

A/Q

We are given that one zero is negative and one positive, hence their sum is equal to 0.

--> Sum of zeroes = -b/a

Solving for k :-

--> 8k/4 = 0

--> 8k = 0

--> k = 0

•°• Value of k is 0.

Answer 2

→ Given ←

One zero of the polynomial 4x² - 8kx - 9 is negative of the other zero.

◙ If α and β are the 2 zeros, then :-

α = -β

$\rule{180}2$

→ To Find ←

The value of 'k'.

$\rule{180}2$

→ Solution ←

From the relation, we get :-

α = β

We know,

◙ Sum of the zeros = α + β = -b/a

⇒α + β = 8k/4

⇒α + (-α) = 2k

⇒α - α = 2k

⇒0 = 2k

⇒k = 0/2

⇒k = 0

Therefore, the value of k is 0.