Question

if a and B are the zeoes of the polynomial f (x) = X2 - 4x + k such that a- b = 2, find the value of k.

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Answer 1

Answer:

k=-1

k=2/3

Step-by-step explanation:

Here is your answer,

kx^2 + 4x + 4=0

Sum of zeroes = -b/a

a+b = -4/k

Product of zeroes =c/a

ab = 4/k

It is given that,

a^2 + b ^2 =24

(a+b)^2 -2ab =24

(-4/k)^2 -2x4/k =24

16/k^2 - 8/k=24

16-8k/k^2 =24

24k^2 +8k -16=0

Here is a quadratic equation.

Solve it to find the value of k.

Divide the equation by 8.

3k^2 +k -2=0

3k^2 +3k -2k -2=0

3k (k+1) -2(k+1)=0

(K+1)+(3k-2)=0

k=-1

k=2/3

Hope it helps you!