Question

If sum and product of zeros are -2 and 1/3 what is the quadratic polynomial??

Answer 1

Step-by-step explanation:

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Answer 2

Given :

• α + β = -2 [ Given ]
• α × β = 1/3 [ Given ]

To Find :

The quadratic polynomial

Theory :

if $\sf\alpha \: and \beta$ are the zeros of a quadratic polynomial f(x) . Then the polynomial f( x) is given by

$\sf \:f(x) = k(x {}^{2} - ( \alpha + \beta )x + \alpha \beta )$

or

$\sf \: f(x) = k(x {}^{2} - (sum \: of \: the \: zeroes)x + product \: of \: the \: zeroes)$

Solution :

Let the polynomial ax² + bx + c and its zeroes be α and β.

Here,

α + β = -2 [ Given ]

α × β = 1/3 [ Given ]

We know that,

For the quadratic polynomial:

$\sf \: f(x) =k( x {}^{2} - ( \alpha + \beta )x + \alpha \beta )$

Now,

Polynomial formed:

$\sf\:f(x) =k(x{}^{2}-(-2)x+\dfrac{1}{3})$

$\sf\:f(x) =k(x^2+4x+\dfrac{1}{3})$

If k = 3,then

Polynomial=$\sf\:f(x)(x^2+4x+\dfrac{1}{3})$$\bf\:f(x)=3x^2+12x+1$

Therefore, One quadratic polynomial which satisfy the given conditions is 3x² + 12x + 1