Question

Question: 7
If one of the zero of the quadratic polynomial f(x) = 4x2 – 8kx – 9 is negative of the other, then find the value of zeroes.. ​

Answer 1

Heya!!

Given Quadratic polynomial is

F(x) = 4x² - 8kx - 9

This Quadratic polynomial has two roots, as its maximum degree is two.

Let those two roots be a and b

It is given that one root is negative of other I,e a = -b

a + b = 8k/4

a + ( - a ) = 8k/4

a - a = 8k/4

8k/4 = 0

2k = 0

k = 0

So, For one root Equal to negative of another root the value of k is 0

Answer 2

Solution:

Let, the two zeroes of the polynomial f(x) = 4x2 – 8kx – 9 be α and − α.

Product of the zeroes = α × − α = – 9

Sum of the zeroes = α + (− α) = – 8k = 0 Since, α – α = 0

⇒ 8k = 0 ⇒ k = 0