Question

Write the quadratic polynomial, the sum and product of whose zeroes are -9/2 and-3/2 respectively.

Answer 1

Given :- Write the quadratic polynomial, the sum and product of whose zeroes are -9/2 and-3/2 respectively.

Solution :-

we know that, the quadratic equation can be written as ,

• x² - (sum of roots)x + product of roots = 0 .

we have,

• sum of roots = (-9/2)
• product of roots = (-3/2) .

then,

→ Required quadratic polynomial :- x² - (-9/2)x + (-3/2) = 0

→ Required quadratic polynomial :- x² + (9x/2) - (3/2) = 0

→ Required quadratic polynomial :- (2x² + 9x - 3) / 2 = 0

→ Required quadratic polynomial :- 2x² + 9x - 3 = 0 (Ans.)

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Answer 2

SOLUTION

TO DETERMINE

The quadratic polynomial, the sum and product of whose zeroes are -9/2 and-3/2 respectively.

CONCEPT TO BE IMPLEMENTED

If the Sum of zeroes and Product of the zeroes of a quadratic polynomial is given then the quadratic polynomial is

$\sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }$

EVALUATION

Here it is given that for the given Quadratic polynomial

$\displaystyle\sf{ Sum \: of \: the \: zeroes = - \frac{9}{2} }$

$\displaystyle\sf{ Product \: of \: the \: zeroes = - \frac{3}{2} }$

Hence the required Quadratic polynomial is

$\displaystyle\sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }$

$= \displaystyle\sf{ {x}^{2} - \bigg( - \frac{9}{2} \bigg)x - \frac{3}{2} }$

$= \displaystyle\sf{ {x}^{2} + \frac{9x}{2} - \frac{3}{2} }$

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