Question

if the zeroes of the quadratic polynomial x^2+(m+1)x + n are 4 and 5 then​

Answer 1

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Answer 2

SOLUTION

CORRECT QUESTION

GIVEN

The zeroes of the quadratic polynomial x² + (m + 1)x + n are 4 and 5

TO DETERMINE

The value of m and n

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 4 and 5

Sum of the zeroes = 4 + 5 = 9

Product of the zeroes = 4 × 5 = 20

So the polynomial with zeroes 4 and 5

$\sf = {x}^{2} - 9x + 20$

Now the given polynomial

$\sf = {x}^{2} + (m + 1)x + n$

On comparison we get

m + 1 = - 9 and n = 20

Consequently we have m = - 10 and n = 20

FINAL ANSWER

The value : m = - 10 and n = 20

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