Question

If the sum of zeros of quadratic polynomial p(x) = px² - 4x + 2k is same as their product Find k​

Answer 1

Step-by-step explanation:

Given :-

The sum of zeros of quadratic polynomial p(x) = px² - 4x + 2k is same as their product .

To find :-

Find the value of k ?

Solution :-

Given Quadratic Polynomial is p(x) = px² - 4x + 2k

On comparing this with the standard quadratic Polynomial ax²+bx+c

We have

a = p

b = -4

c = 2k

We know that

Sum of the zeroes = -b/a

=> -(-4)/p

=> 4/p

Sum of the zeores = 4/p ----------(1)

Product of the zeroes = c/a

=> 2k/p

Product of the zeroes = 2k/p ------(2)

Given that

The sum of zeros of quadratic polynomial p(x) = px² - 4x + 2k is same as their pproduct

=> (1) = (2)

=> 4/p = 2k/p

On applying cross multiplication then

=> 2k×p = 4×p

=> 2k = 4×p/p

=> 2k = 4

=> k = 4/2

=> k = 2

Therefore, k = 2

Answer:-

The value of k for the given problem is 2

Used formulae:-

• The standard quadratic Polynomial is ax²+bx+c

• Sum of the zeroes = -b/a

• Product of the zeroes = c/a