Question

Find the quadratic polynomial whose zeroes are -4 snd3 by 2

Answer 1

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♣ Given :-

For a Quadratic Polynomial

   

• First Zero = - 4

• Second Zero = 3/2

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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 = - 4 + 3/2 = - 2/5

Product = p = - 4 × 3/2 = - 6

So,

Required Polynomial should be

$\bf{x}^{2}  - \bigg(-\dfrac{2}{5} \bigg)x + (-6)$.

$\Large\purple{:\longmapsto\pmb{5 {x}^{2}  +2x -30}}$

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

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Answer 2

Answer:

Here's your answer

Step-by-step explanation:

Given => let one zero be α=-4

               let other zero be β=3/2

So,ACC to the ques

We have to form a quadratic polynomial

So,

(α+β)=-4+3/2

       = -8+3/2

        = -5/2

(αβ) = -4*3/2

       = -12/2

        = -6

Now ,

p(x)=K[x^2-(α+β)x-(αβ)]

p(x)=K[x^2-(-5/2)x-(-6)

Taking 2 from -5/2 at the place of K

p(x)=2[x^2+5x+6]

So,our final quadratic polunomial will be,

p(x)=2x^2+10x+12

Hope you understand.