Question

Find a quadratic polynomial whose zeroes are 2 and -6.
a. x2+4x+12
b. x2-4x-12
c. x2+4x-12
d. x2-4x+12




If α, β, are the zeroes of the polynomial p(x) such that α+β+γ=3, αβ+βγ+γα=10, αβγ=-24, then px=?




a. x3+3x2-10x+24
b. x3-3x2+10x+24
c. x3-3x2-10x-24
d. x3+3x2+10x-24

Answer 1

Answer:

b. x2-4x-12

b.x3-3x2+10x+24

Answer 2

$\huge \mathcal{Part \: 1} : -$

▪ Given :-

For a Quadratic Polynomial

   

• 1 st Zero = 2

• 2nd Zero = -6

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▪ To Find :-

• The Quadratic Polynomial.

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▪ Key Point :-

If sum and product of zeros of any quadratic polynomial are s and p respectively,

Then,

The quadratic polynomial is given by :-

$\bf  {x}^{2}  - s \: x + p$

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▪ Solution :-

Here,

Sum = s = - 6 + 2 = - 4

and

Product = p = - 6 × 2 = - 12

So,

Required Polynomial should be

$\bf{x}^{2}  - (-4)x +  -12$

$\longmapsto \Large\bf  {x}^{2}   +4x-12$

$\color{magenta}{ \large \mathfrak{Option \: \: \text{C } \: \: is \: \: Correct }}$

$\Large \red{\mathfrak{  \text{W}hich \:   \: is  \:  \: the  \:  \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswer.}}$

___________________________

$\huge \mathcal{Part \: 2} : -$

▪ Correct Question :-

If α, β,γ are the zeroes of the polynomial p(x) such that α+β+γ=3, αβ+βγ+γα=10, αβγ=-24, then px=?

___________________________

▪ Given :-

α, β,l and γ are the zeroes of the polynomial p(x) such that :

• α+β+γ=3

• αβ+βγ+γα=10

• αβγ=-24

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▪ To Find :-

• The Polynomial p(x)

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▪ Key Point :-

A cubic polynomial whose zeros are α , β & γ

is of the Form

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

▪Solution :-

Here,

• α+β+γ=3

• αβ+βγ+γα=10

• αβγ=-24

So, Polynomial Should be :

$\bf{x}^{3}  - 10x^2+4x +  24$

$\color{magenta}{ \large \mathfrak{Option \: \: \text{B} \: \: is \: \: Correct }}$

$\Large \red{\mathfrak{  \text{W}hich \:   \: is  \:  \: the  \:  \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswer.}}$

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