Question

Determine the value of a and b if polynomial 2 x cube + x square - 14 x + b has the sum of its zeros as 5.2 and the product of its zeros as - 4

Answer 1

Answer:

a= -10.4,b =8

Step-by-step explanation:

let a cubic equation be

ax3 + bx2 + cx + d=0

let the roots be p,q,r

a(x−p)(x−q)(x−r)

= ax3 − a(p+q+r)x2 + a(pq+pr+qr)x − a(pqr).......(1)

given equation 2x3+Ax2-14x+B=0......(2)

given p+q+r=5.2, pqr = -4

comparing both equation (1) and (2)

A= -a(p+q+r)= -2×5.2 = -10.4

B= -a(pqr)= -2(-4)= 8