Flag 10 grade maths> If alpha and beta are the zeroes of the p...
question mark

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

S. Haris Ahmed Irfan , 10 Years ago
Grade 12
anser 1 Answers
SHAIK AASIF AHAMED

Last Activity: 10 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

Provide a better Answer & Earn Cool Goodies

Enter text here...
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Enter text here...