Question

If alpha and beta are zeros of the polynomial kx^2+3x+2 and alpha ^2+beta^2+alpha*beta=-1/25 then find k

Answer 1

Given, α and β are the zeroes of the given polynomial kx2 + 4x + 4.

⇒ 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

⇒ 3k – 2 = 0 or k + 1 = 0

Answer 2

alpha+beta=-b/a

alpha+beta=-3/k

alpha*beta=c/a

alpha*beta=2/k

#alpha^2+beta^2=(alpha+beta)^2-2alpha*beta

so,

(alpha+beta)^2-2alpha*beta+alpha*beta

(alpha+beta)^2-alpha*beta=-1/25

putting up the values

(-3/k)^2-(2/k)=-1/25

9/k^2 -2/k=-1/25

lcm=k^2

9-2k/k^2=-1/25

25(9-2k)=-k^2

225-50k=-k^2

k^2-50k+225=0

u can solve now....