Question

if a and b are the zeroes of the quadratic polynomial x²-kx+15 such that (a+b)²-2ab=34,find 'k'

Answer 1

Hey!

Given Equation :- x² - kx + 15
Given Condition :- ( a + b )² - 2ab = 34


• Sum of Zeros =

$= \frac{ - coefficient \: \: of \: \: x}{coefficien \: \: of \: \: {x}^{2} }$

a + b = k/1


• Product of Zeros =
$= \frac{constant \: \: term}{coeff. \: \: of \: {x}^{2} }$


ab = 15

Now , from given condition :-


( a + b )² - 2ab = 34

( k )² - 2 × 15 = 34

k² - 30 = 34

k² = 34 + 30

k² = 64

k = √64

k = ± 8


So, the value of k is ±8 for the Equation !!

Answer 2

➡ Given polynomial :-- x2 - kx + 15 .

according to formulas .:;

sum of zero = k .

& product of zero -- 15 .


➡ ( a + b )2 - 2ab. = 34 .

k2 - 30 = 34 .

➡ k2= 64.

therefore , k = 8 . ⬆⬆⬆..:-)
hope it's helpful !!