Question

If sum of the squares of zeroes of the quadratic
polynomial p(x) = x2 - 10x + 2k is 28, find the
value of k.
(a) 18
(b) 14
(c) 16
(d) 20​

Answer 1

Answer:

a. k = 18 .

Verified by calculations.

Step-by-step explanation:

Hope it helps...

Answer 2

$\sf\underline{Answer:}$

Option a ; 18 is the value of k

$\sf\underline{Explanation:}$

Given, sum of squares of zeroes of the quadratic polynomial p(x) is 28.

Let the zeroes be alpha and beta (general notation for zeroes).

The polynomial is $p_{(x)} = {x}^{2} - 10x + 2k$

a = coefficient of x^2 ; b = coefficient of x ; c = constant

${ \alpha }^{2} + { \beta }^{2} = 28$

→ Sum of the zeroes = alpha + beta

$\alpha + \beta = \frac{ - b}{a} = \frac{ - ( - 10)}{1}$

$\alpha + \beta = 10$

→ Product of zeroes = alpha × beta

$\alpha \beta = \frac{c}{a} = \frac{2k}{1}$

$\alpha \beta = 2k$

→ Let's consider the sum of zeroes and square them on both sides

${( \alpha + \beta )}^{2} = {10}^{2}$

${ \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta = 100$

$28 + 2(2k) = 100$

$4k = 72$

$k = 18$

Have a good day!