Question

A quadratic polynomial whose zeroes are -3 and 4 is
a) x2 - x + 12
b) x2 + x + 12
c) x2/2 - x/2 - 6
d) 2x2 - 2x -24

Answer 1

$\large \bf \clubs \:  Given :-$

For a Quadratic Polynomial :

• First Zeros = -3

• Second Zeros = 4

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$\large \bf \clubs \:   To  \: Find :-$

• The Quadratic Polynomial.

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$\large \bf \clubs \:   Main  \:  Concept : -$

☆ If sum and product of zeros of any quadratic polynomial are S and P respectively, Then,

The polynomial is given by :-

$\bf  {x}^{2}  - S \: x + P$

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$\large \bf \clubs \:  Solution  :-$

Here,

• Sum = S = -3 + 4 = 1

• Product = P = -3 × 4 = -12

So,

Required Polynomial should be :

$:\longmapsto\bf  {x}^{2}  - S \: x + P$

$:\longmapsto{x}^{2}  - (1) x +(-12)$

$\large:\longmapsto {x}^{2}  - x -12$

✏ Multiplying By 2 :

$\Large\purple{:\longmapsto\pmb{{2x}^{2}  -2x -24}}$

Hence,

$\Large \underline{\pink{\underline{\pmb{\frak{Option \: \text{d} \: is\:Correct}}}}}$

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Answer 2

Given :-

Zeroes = -3 and 4

To Find :-

Quadratic polynomial

Solution :-

We know that

Sum of zeroes = α + β &

Product of zeroes = αβ

Let α = 4 and β = -3

Sum = 4 + (-3)

Sum = 4 - 3

Sum = 1

Product = 4 × (-3)

Product = -12

Standard form of quadratic polynomial = x² - (α + β)x + αβ

x² - (1)x + (-12)

x² - x - 12

Hmm, Not getting correct option. Let multiply the equation by 2

2(x² - x - 12)

2x² - 2x - 24

Therefore,Option D is correct