Question

Find the cubic polynomial 4x3+10x2+6x and verify the relationship between the zeros and the coefficient

Answer 1

Answer:

Step-by-step explanation:

Given equation:$4x3+10x2+6x$

Take 2x common from the polynomial.

$2x(2x^{2} +5x+3)$

so, we get the first zero(say α) ⇒2x=0⇒x=0

now,solve the quadratic polynomial in the bracket,

$(2x^{2} +5x+3)=0$

by prime factorisation,

⇒$2x^{2} +2x+3x+3=0$                     [∵2×3=6 and 2+3=5]

⇒$2x(x+1)+3(x+1)=0$

we get,$(2x+3)(x+1)$

Thus the other two zeroes(say β and ω) are

(-3/2) and (-1)

verification→

α+β+ω=0-3/2-1=(-5/2)

also,-b/a=(-10/4)=(-5/2)

αβ+βω+ωα=0+(-3/2×-1)+0=3/2

also,c/a=6/4=3/2

αβω=0×-3/2×-1=0

also,-d/a=0/4=0

Hence verified.

hope it helps.