Question

.Write the cubic polynomial whose zeroes are 1, -3 & 2.​

Answer 1

EXPLANATION.

Cubic polynomial.

Whose zeroes are = 1, - 3 and 2.

As we know that,

Let one zeroes be = α = 1.

One zeroes be = β = - 3.

One zeroes be = γ = 2.

Sum of the zeroes of the cubic polynomial.

⇒ α + β + γ = - b/a.

⇒ (1) + (-3) + 2.

⇒ 1 - 3 + 2 = 0.

⇒ α + β + γ = 0. - - - - - (1).

Products of the zeroes of the cubic polynomial two at a time.

⇒ αβ + βγ + γα = c/a.

⇒ (1)(-3) + (-3)(2) + (2)(1).

⇒ - 3 - 6 + 2 = - 7.

⇒ αβ + βγ + γα = - 7. - - - - - (2).

Products of the zeroes of the cubic polynomial.

⇒ αβγ = - d/a.

⇒ (1) x (-3) x (2) = - 6.

⇒ αβγ = - 6. - - - - - (3).

As we know that,

Formula of cubic polynomial.

⇒ x³ - (α + β + γ)x² + (αβ + βγ + γα)x - αβγ.

Put the values in the equation, we get.

⇒ x³ - (0)x² + (-7)x - (-6).

⇒ x³ - 7x + 6.

                                                                                                                   

MORE INFORMATION.

Biquadratic equation.

If α, β, γ, δ are roots of the biquadratic equation ax⁴ + bx³ + cx² + dx + e = 0, then.

σ₁ = α + β + γ + δ = - b/a.

σ₂ = αβ + αγ + αδ + βγ + βδ + γδ = c/a.

σ₃ = αβγ + αβδ + αγδ + βγδ = - d/a.

σ₄ = αβγδ = e/a.

Answer 2

Answer:

$\underline{\purple{\ddot{\Mathsdude}}}$

Answered by Rohith kumar maths dude :-

Explanation: -

Here given that ,

☆Cubic polynomial whose zeroes are 1,-3 and 2.

▪Already we know that,

Let,

one zero be=a=1

one zero be=b=-3

one zero be =c=2

☆As we know that

●Sum of zeroes of cubic polynomial

=a+b+c=-b/a

=1+(-3)+2

=1-3+2

a+b+c=0----(i)

●We know that product of zeroes of cubic polynomial ,

▪ab+bc+ca=c/a

▪=1 (-3)+(-3)(2)+2 (1)

▪-3-6+2=-7

▪ab+bc+ca=-7------(ii)

●Product of the zeroes of cubic polynomial,

abc=-d/a

1 (-3)(2)=-6

abc=-6 -------(iii)

▪We know that,

☆☆Formula of cubic polynomial

x^3-(a+b+c)x^2+(ab+bc+ca)x-abc

Applying the values we get,

x^3-(0)^2+(-7)x-(-6)

=x^3-7x+6.

☆☆Hope it helps u mate .

☆☆Thank you .