Question

-If@ and ß are the zeroes of quadratic polynomial
P(x) = kx2+4x+4 such that a2 +B2=24
Find the value of K.​

Answer 1

Answer:

$\huge\mathfrak\blue{hello}$

Step-by-step explanation:

if.. we take K = 1.. then..

$p(x)= kx {}^{2} + 4x + 4 \\ \: \: \: \: \: \: \: \: \: = (1)x {}^{2} + 4x + 4 \\ \: \: \: \: \: \: \: \: \: = (x + 2)(x + 2) \\ \: \: \: \: \: \: \: \: \: = (x + 2) {}^{2} \\ \: \: \: \: \: \: so \: .... \: x = - 2$

so this Polynomial is right.. if we take K = 1 ..

So K = 1

I hope it will help you...

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Answer 2

Answer:

Step-by-step explanation:

​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

hope this helps you