Question

find a quadratic polynomial the sum of and product of whose zeroes are - 3 and 2 respectively​

Answer 1

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TO DETERMINE

A quadratic polynomial the sum and product of whose zeroes are - 3 and 2 respectively

TO FIND

The quadratic polynomial

FORMULA TO BE IMPLEMENTED

The quadratic polynomial whose zeroes are given can be written as

${x}^{2} - ( \: \: sum \: \: of \: \: the \: \: zeros)x \: + \: \: ( \: product \: \: of \: \: the \: \: zeros)$

EVALUATION

The required Quadratic polynomial is

$= {x}^{2} - ( \: \: sum \: \: of \: \: the \: \: zeros)x \: + \: \: ( \: product \: \: of \: \: the \: \: zeros)$

${x}^{2} - ( - 3)x + 2$

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

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ADDITIONAL INFORMATION

A general equation of quadratic equation is

$a {x}^{2} + bx + c = 0$

Now one of the way to solve this equation is by SRIDHAR ACHARYYA formula

For any quadratic equation

$a {x}^{2} + bx + c = 0$

The roots are given by

$\displaystyle \: x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a}$

Answer 2

Given :

• A quadratic polynomial the sum of and product of whose zeroes are - 3 and 2 respectively.

Find :

• The quadratic polynomial.

Using formula :

★ Quadratic polynomial = x² - (Sum of roots)x + (Product of roots).

Know terms :

1. Sum = Adding.
2. Product = Multiplication.

• Here we are calculating for root.

Solution :

→ x² - (a + b)x + ab = 0

→ x² - (-3)x + 2

• (-) × (-) = (+)

→ x ² + 3x + 2

Therefore, this is the required polynomial.

Know More :

• Some symbols in Integers:

→ (+) × (+) = (+)

→ (+) × (-) = (-)

→ (-) × (+) = (-)

→ (-) × (-) = (+)