Question

Find a quadratic polynomial the sum and difference of whose zeroes are 2and0 respectively

Answer 1

Answer:

Step-by-step explanation:

Let the zeroes of polynomial be α and β

We are given that

α+β= 2___________________________________(1)

α-β= 0_____(A)

so we can say that from equation A

α=β _______________(2)

And so the product of zeroes will be either $\alpha ^{2} or \beta ^{2}$

So my quadratic equation will be

$x^{2} -(\alpha +\beta )x + (\alpha \beta )$

$\implies x^{2} -2x+\alpha ^{2} \\OR\\\implies x^{2} -2x+\beta^{2}$

Answer 2

AnsWer :

x²-2x +1.

Given :

• Sum and difference of whose Zeroes are 2 and 0.

To Find :

Quadratic polynomial.

Solution :

•°• Let first zero be alpha

and second zeros be beta.

A/Q,

$\tt {\fbox{\large{\alpha + \beta = 2.}}} \: \: \: - (1)$

$\tt{\fbox{\large{\alpha - \beta = 0.}}} \: \: \: - (2)$

$\rule{120}1$

Adding Both equation, We get.

$\tt \: \: \: \: \: \: \: \: \: \: \: \alpha + \beta = 2.$

$\tt\underline{ \: \: \: \: \: \: \: \: \: \: \: \alpha - \beta = 0. \: \: \: \: \: \: \: }$

$\tt\: \: \: \: \: \: \: \: \: \: \: 2 \alpha \: \: \: \: \: \: = 2.$

$\tt\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \alpha \: \: \: \: \: \: = 1.\: \: \: \: \: \: \: }$

Now, Putting the value of alpha in equation 1.

$\tt\dashrightarrow \alpha + \beta = 2.$

$\tt\dashrightarrow \beta = 1.$

$\rule{200}2$

We have, Formula to form Quadratic polynomial.

$\tt{\fbox{\large{k( {x}^{2} - sx + p)}}}$

Where as,

• k Constant term.
• s Sum of zeros.
• p product of zeros.

$\tt\dashrightarrow k [ {x}^{2} - ( \alpha + \beta ) x + ( \alpha \beta )]$

$\tt\dashrightarrow k( {x}^{2} - 2x + 1).$

Therefore, Our Equation become x²- 2x +1.