Question

If -2 and three are the zeros of quadratic polynomial X square plus a plus 1X plus B then

Answer 1

SOLUTION

GIVEN

- 2 & 3 are the zeros of quadratic polynomial

$\sf{ {x}^{2} + (a + 1)x + b}$

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

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

TO DETERMINE

The value of a and b

EVALUATION

Here it is given that

- 2 & 3 are the zeros of quadratic polynomial

Then the quadratic polynomial is

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

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

$\sf{ = {x}^{2} - x + 6}$

Again the given Quadratic polynomial is

$\sf{ {x}^{2} + (a + 1)x + b}$

Comparing we get

a + 1 = - 1 & b = 6

⇒ a = - 2 & b = 6

FINAL ANSWER

Hence the required value of a and b are - 2 & 6 respectively

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