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If alpha and beta are the zeroes of the polynomial kx^2+4x+4. Show that (alpha)^2+(beta)^2=24. find the value of k

If alpha and beta are the zeroes of the polynomial kx^2+4x+4. Show that (alpha)^2+(beta)^2=24. find the value of k

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Please find the answer to your question below
Givenalpha and beta are the zeroes of the polynomial kx^2+4x+4
I 'll denote alpha by x and beta by y.
x + y = -b/a
x+y=-4/k.......eq 1
xy= c/a
xy= 4/k........eq 2
Squaring both sides of eq 1
(x+y)2= (-4/k)2
x2+y2+2xy=16/k2
24+2xy=16/k2 [from x2+y2 = 24]
Substituting the value of xy from eq2,
24+2*4/k=16/k2
24+8/k=16/k2
24k+8/k=16/k2
24k+8=(16/k2)*(k)
24k+8=16/k
24k2+8k=16
or 24k2+8k -16=0
3k2+k-2=0
3k2+3k-2k-2=0
3k(k+1)-2(k+1)=0
(3k-2)(k+1)=0
Therefore,k is either -1 or 2/3

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