Question

find the quadratic polynomial whose zeroes are -2 and -5.Verify the relationship between their zeroes and coefficients​

Answer 1

let the zeros be alpha and beta
then,
f(x) = x^2 - (alpha+ beta)x +alpha•beta
=x^2 -{-2+(-5)}x + (-2)(-5)
= x^2 +7x + 10

Verification:
sum of zeros = -b/a
=> -2 + (-5) = -7/1
=> -7 = -7
L.H.S = R.H.S

Product of zeros = c/a
=> (-2)(-5) = 10/1
=> 10 = 10
L.H.S = R.H.S


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Answer 2

given :-

zeroes =  -2  and -5

now ,

sum of zeroes = -2 +( -5 ) = -7 = coefficient of x / coefficient of x^2 = -b/ a

product of zeroes = -2 * -5 = -10 = constant term / coefficient of x^2 = c /a

so , the equation will be

x^2 + 7x - 10