1. If α and β are zeroes of x2 - 4x + 1, then find:
a) 1/α + 1/β
b) α2 + β2
c)1/α+1/β+αβ
2. α and β are zeroes of x2 +(kx +6)x +(4k-2), then find the value of k if-
3.
a) roots are reciprocal of each other b) if α+ β = α β
4.
If one zero of the quadratic polynomial p(x)= x2 + 4kx- 25 is negative of the other, find the value of k.
Find a quadratic polynomial whose zeros are 2 and -6.
Answers
Answer:
You have to mark my answer as brainliest
Step-by-step explanation:
1. The given quadratic equation,
x^2-4x+1
Comparing to the general quadratic equation,
ax^2+bx+c
Where,
a= 1, b= -4, c= 1
Given that α and β are zeroes of the polynomial.
From the properties of the zeroes.
Then,
=4-1
=3
2. in the photo
4. Let the first zero be "a"
and second zero be "-a"
sum of zeroes = -b/a
a + (-a) = (8k²-40k)/4
a - a = 2k²-10k
0 = 2k²-10k
0 = 2k (k -5)
2k = 0 , k - 5 = 0
k = 0,. K = 5
hence, k = 5,0
1) Given : α and β are zeroes of x² - 4x + 1;
So, Let's find out relationship between Zeroes.
↪ Sum of Zeros = -b/a
= 4 / 1
= 4
↪ Product of Zeros = c/a
= 1/1
= 1
Now, Solving Query !
1/α + 1/β - αβ
= ( α + ß/ aß ) - aß
= α + ß - ( aß )² / aß
= 4 - ( 1 )² / 1
= 4 - 1 / 1
= 3
Therefore, Value of 1/α + 1/β - αβ is 3...
2)