Question

a
B
7. If one zero of the quadratic polynomial
find the value of k.
v or the quadratic polynomial f(x) = 4x2 – 8kx - 9 is negative ​

Answer 1

Correct Question

If one zero of the quadratic polynomial f(x) = 4x² - 8kx - 9 is negative of the other zero then, find the value of k.

Answer

k = 0

Explanation-

Let us assume that the zero of the quadratic polynomial is x.

One zero of the quadratic polynomial is negative of the other. So, the other zero is -x.

Therefore, assumed zeros of the quadratic polynomial f(x) = 4x² - 8kx - 9 are (x) and (-x).

Now, the given quadratic polynomial is in the form ax² + bx + c.

Where; a = 4, b = -8k and c = -9

We have to find the value of k.

We know that,

Sum of zeros = -b/a and Product of zeros = c/a

So,

Sum of zeros = -b/a

→ x + (-x) = -(-8k)/4

→ x - x = 8k/4

→ 0 = 2k

→ 0/2 = k

→ k = 0

Answer 2

Given :-

• Quadratic polynomial f(x) = 4x² - 8kx - 9 = 0
• one zero of the quadratic polynomial is Negative of other zero.

To Find :-

• value of k ?

concept used :-

• The sum of the roots of the Equation ax² + bx + c = 0 , is given by = -(coefficient of x)/coefficient of x² = (-b/a)

Solution :-

Comparing The given Polynomial 4x² - 8kx - 9 = 0 with ax² + bx + c = 0 we get ,

⟼ a = 4

⟼ b = (-8k)

⟼ c = (-9)

Let us Assume That, Zeros of the Given quadratic polynomial are ɑ & β .

⟿ ɑ = (-β) (Given) . ---------- Equation ❶

Now,

➪ sum of zeros = (-b/a)

➪ ɑ + β = -(-8k/4)

Putting value of ɑ from Equation ❶ in LHS , we get,

➪ (-β) + β = 2k

➪ 0 = 2k

➪ 2k = 0

➪ k = 0 (Ans.)

•°• value of k will be zero.