Question

If the zeros of the quadratic polynomial x square + (a + 1) close x + br2 and minus 3 then find the value of a and b

Answer 1

SOLUTION

GIVEN

The zeros of the quadratic polynomial

x² + (a + 1)x + b are 2 and - 3

TO DETERMINE

The value of a and 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

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

EVALUATION

Here the given zeroes are - 2 & 3

So the polynomial is

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

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

Now the given polynomial is x² + (a + 1)x + b

Comparing we get

a + 1 = 1 and b = - 6

⇒ a = 0 and b = - 6

FINAL ANSWER

a = 0 and b = - 6

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