Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively. About the author Quinn
Answer: Let the polynomial be ax 3 +bx 2 +cx+d and the zeroes be α,β,γ. Sum of the polynomial = α+β+γ= 1 2 = a −b Sum of the product of its zeroes taken two at a time = αβ+βγ+αγ= 1 −7 = a c Product of the root = αβγ= 1 −14 = a −d If a=1,b=−2,c=−7,d=14. Hence the polynomial is x 3 −2x 2 −7x+14 Reply
Answer:
Let the polynomial be ax
3
+bx
2
+cx+d and the zeroes be α,β,γ.
Sum of the polynomial = α+β+γ=
1
2
=
a
−b
Sum of the product of its zeroes taken two at a time = αβ+βγ+αγ=
1
−7
=
a
c
Product of the root = αβγ=
1
−14
=
a
−d
If a=1,b=−2,c=−7,d=14.
Hence the polynomial is x
3
−2x
2
−7x+14