Question

if the sum of product of their zeros are -3 & 2respectievely,then the quadratic polynomial is​

Answer 1

GIVEN:

• Sum of the zeroes = -3
• Product of the zeroes = 2

TO FIND:

• Find the quadratic polynomial ?

SOLUTION:

We have given that, the sum of zeroes and the product of zeroes are -3 and 2 respectively.

☞ We have to find the quadratic polynomial

To find the quadratic polynomial, we use the equation:-

❮ x² – (Sum of zeroes)x + Product of zeroes ❯

$\large\bf{\star \: x^2 -sx + p \: \star}$

According to question:-

On putting the given values in the formula, we get

$\rm{\dashrightarrow x^2 -(-3)x + 2 }$

$\bf{\dashrightarrow x^2 + 3x + 2}$

❝ Hence, the quadratic polynomial formed is x² + 3x + 2 ❞

____________________________

✯ Extra Information ✯

➣ Formation of linear polynomial = x - $\bold{ \alpha}$

➣ Formation of cubic polynomial = x³ – sx² + s'x – p

➣ Zero polynomial = p(x) = 0

[ Number zero itself is known as zero polynomial ]

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \pink{Question:-}}}}}}$

If the sum of product of their zeros are -3 & 2 Respectively .. Then the quadratic polynomial is?

______________________

${ \huge{ \bold{ \underline{ \underline{ \green{Answer:-}}}}}}$

✒Given :

• Sum of zeroes $(\alpha+\beta)$=-3
• Product of zeroes $(\alpha\beta)=2$

✒To Find :

• Quadratic Polynomial = ?

✒Formula Used :

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

$\dashrightarrow\sf{{x}^{2}-(-3) x+(2)}$

$\dashrightarrow\sf{{x}^{2}+3x+2}$

✎So, the Quadratic Polynomial is x² + 3x + 2 ..