Question

if roots of equation 4x³-12x²+11x+k=0 are in arthimetic progression then k=​

Answer 1

For this polynomial

Sum of roots =12/4 = 3

=(a-d)+(a)+(a+d)

=3a=3

->a=1

a(a-d)+a(a+d)+(a-d)(a+d)=11/4

=2a^2 +a^2 -d^2 =2.75

=3a^2 - d^2 =2.75

=3-d^2 =11/4

=d^2 =3–11/4=1/4

=d=±1/2

Hence roots are 1/2,1,3/2

So product of roots is 3/4

-k/4=3/4

k=-3

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