If the sum of zeroes of the
polynomial x2 - x - k(2x- 1) is zero find the value of
k.
Answers
Answered by
109
for a quadratic ax² + bx + c = 0
so we know sum of roots = -b /a
product of roots = c/a
let roots of the eq x² - x - k(2x- 1) ⇒ x² - x - 2kx +k ⇒ x² - (1 - 2k)x +k
be x , y
so given x+ y = 0
so (1 - 2k )/1 = 0
⇒ k = 1/2
so we know sum of roots = -b /a
product of roots = c/a
let roots of the eq x² - x - k(2x- 1) ⇒ x² - x - 2kx +k ⇒ x² - (1 - 2k)x +k
be x , y
so given x+ y = 0
so (1 - 2k )/1 = 0
⇒ k = 1/2
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Answered by
36
First of all you must know that any quadratic equation can be written as :
Note: This is a very powerful tool. Do remember it.
X^2 -sx+p -----------------(i)
where s is the sum of its roots and p is their product.
On comparing your equation , we get
p=k
s=2k+1
As we had only to talk about their sum so
It is given that s=0
This means that 2k+1=0
2k=-1
k=-1/2.
Note: This is a very powerful tool. Do remember it.
X^2 -sx+p -----------------(i)
where s is the sum of its roots and p is their product.
On comparing your equation , we get
p=k
s=2k+1
As we had only to talk about their sum so
It is given that s=0
This means that 2k+1=0
2k=-1
k=-1/2.
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