Question

the quadrati polynomial whose zeroes are 4 and 1​

Answer 1

Answer:

General form of a quadratic polynomial is x^2-sx+p; here s is sum of zeroes & p is product of zeroes.

sum of zeroes=4+1=5

product of zeroes=4×1=4 therefore,polynomial is

x^2-5x+4

Answer 2

Answer:

The quadratic polynomial whose zeroes are $4$ and $1$ is  $x^2- 5x + 4 = 0$ .

Step-by-step explanation:

If $\alpha$ and $\beta$ are the roots of the equation then the quadratic equation will be

 $x^2- (\alpha +\beta )x + \alpha \beta = 0$.

where    $\alpha + \beta$ is Sum of the roots

              $\alpha \beta$     is Product of the roots

Step 1:

Here, according to the question, $\alpha = 4$  and $\beta = 1$.

Sum of roots        $\implies \alpha + \beta = 4 + 1$

                                              $= 5$

Product of roots   $\implies \alpha \beta = 4 . 1$

                                           $=4$

Step 2:

Putting the values in the general form of the equation i.e $x^2- (\alpha +\beta )x + \alpha \beta = 0$  , we get   $x^2- 5x + 4 = 0$ .

Hence, the quadratic polynomial whose zeroes are $4$ and $1$ is  $x^2- 5x + 4 = 0$ .

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