III. Answer the following :(3 x 2 = 6m )
9. If ∝ and are two zeroes of the polynomial kx 2 + 4 x + 4 such that ∝ 2 + = 24 , then find the value of k .
10. If ∝ and are two zeroes of the polynomial x 2 - 5x + 6 , find a quadratic polynomial whose zeroes are 2 ∝+ 1 and 2 + 1
IV. Answer the following : (4 x 1 =4m )
11. Find the zeroes of the polynomial x 2 - 6x - 27 and verify the relationship between the zeroes and their coefficients ?
Answers
Solution :- α and β are the zeros of the given polynomial Kx² + 4x + 4 = 0
so, product of zeros = αβ = constant/coefficient of x² = 4/K
sum of zeros = α + β = -coefficient of x/Coefficient of x² = -4/k
Now, α² + β² = 24
⇒(α + β)² - 2αβ = 24
⇒(-4/k)² - 2(4/k) = 24
⇒16/K² - 8/k = 24
⇒ 2 - k = 3k²
⇒3k² + k -2 = 0
⇒ 3k² + 3k - 2k - 2 = 0
⇒3k(k + 1) - 2(k +1) = 0
⇒(3k -2)(k + 1) = 0
Hence, k = 2/3 and -1
2.Which having the zeroes, and .
For finding the zeroes,
Thus, the zeroes of the given quadratic equation are 2 and 3,
3.hope this attachment helps you
please mark has branliest
Answer:
9 & 11 Answer refer my Bro Answer @ Manojkeerhana
Explanation:
10....x²-5x+6=0
(x-2)(x-3)=0
x=2,3
alpha=2
beta=3
x²+(alpha+beta)+(alpha.beta)
roots are 2alpa+1=2×2+1=5,2beta+1=2×3+1=7
x²+(5+7)x+(5×7)=0
x²+12x+35=0 is the answer