find a quadratic polynomial the sum and product of whose zeroes are -7 & -18 respectively.Hence find the zeroes
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Answer:
sum of zeros (a+b) = -7
product of zeros (ab) = -18
from the formula to find quadratic polynomial
x²- (a+b)x+ ab
x²- (-7+(-18))x +(-7)(-18)
x²-(-7-18)x + 126
x²-(-25)x + 126
x²+25x+126 is the quadratic polynomial of the given zeros -7&-18
and the zeros we get is -7 & -18 as given in the question but if you need to verify it
then
x²+ 25x +1 26=0
x²+ 18x + 7x +126=0
x(x+18) + 7(x+18)=0
(x+7)(x+18)=0
x+7=0 or x+18= 0
x= -7 or x= -18
hence in the question there were same zeros after verification
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sum of zeroes =-7
products of zeroes =-18
quadratic formula for making polynomial -
K [x^2-(α+β )x+β ]=0
K [x^2+7x-18]=0
x^2+7x-18=0
x^2+7x-18=0
x^2+(9-2)x-18=0
x^2+9x-2x-18=0
x(x+9)-2 (x+9)=0
(x+9) (x-2)=0
zeroes are x=-9 or x=2
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