Question

Write the quatratic polynomial whose sum and product of zeroes are -3,2​

Answer 1

$\huge\tt{\red{\underline{Given:}}}$

★Sum of zeroes of a Quadratic polynomial is -3

★Product of zeroes of a quadratic polynomial is 2 .

$\huge\tt{\red{\underline{To\:\:Find:}}}$

★The quadratic polynomial.

$\huge\tt{\red{\underline{Concept\:\:Used:}}}$

★We would use a general formula for finding the quadratic polynomial when sum and product of it's zeroes are given.

$\huge\tt{\red{\underline{Answer:}}}$

Let

• $\alpha$ as the first zero
• $\beta$ as the second zero.

By question,

$\green{\boxed{\alpha+\beta =(-3) }}$

$\green{\boxed{\alpha\beta =2 }}$

______________________________________

Now we know that when sum and product of zeroes is given we can use this formuala for finding quadratic polynomial i.e.

Let the polynomial be p(x).

$\large\purple{\boxed{p(x) =x^{2}-x(\alpha+\beta) +\alpha\beta}}$

On substituting the values,

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

$\implies p(x) =x^{2}-x(-3) +2$

$\implies p(x) = x^{2}+3x+2$

. °. ${\underline{\boxed{p(x) =x^{2}+3x+2}}}$

Therefore the required quadratic polynomial is

$x^{2}+3x+2$.

$\huge\orange{\boxed{p(x)=x^{2}+3x+2}}$

Answer 2

Answer:

★Sum of zeroes of a Quadratic polynomial is -3

★Product of zeroes of a quadratic polynomial is 2 .

\huge\tt{\red{\underline{To\:\:Find:}}}

ToFind:

★The quadratic polynomial.

\huge\tt{\red{\underline{Concept\:\:Used:}}}

ConceptUsed:

★We would use a general formula for finding the quadratic polynomial when sum and product of it's zeroes are given.

\huge\tt{\red{\underline{Answer:}}}

Answer:

Let

\alphaα as the first zero

\betaβ as the second zero.

By question,

\green{\boxed{\alpha+\beta =(-3) }}

α+β=(−3)

\green{\boxed{\alpha\beta =2 }}

αβ=2

______________________________________

Now we know that when sum and product of zeroes is given we can use this formuala for finding quadratic polynomial i.e.

Let the polynomial be p(x).

\large\purple{\boxed{p(x) =x^{2}-x(\alpha+\beta) +\alpha\beta}}

p(x)=x

2

−x(α+β)+αβ

On substituting the values,

\implies p(x) =x^{2}-x(\alpha+\beta) +\alpha\beta⟹p(x)=x

2

−x(α+β)+αβ

\implies p(x) =x^{2}-x(-3) +2⟹p(x)=x

2

−x(−3)+2

\implies p(x) = x^{2}+3x+2⟹p(x)=x

2

+3x+2

. °. {\underline{\boxed{p(x) =x^{2}+3x+2}}}

p(x)=x

2

+3x+2

Therefore the required quadratic polynomial is

x^{2}+3x+2x

2

+3x+2 .

\huge\orange{\boxed{p(x)=x^{2}+3x+2}}

p(x)=x

2

+3x+2