question no. 4 plz answer urgent
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let's first check its discriminant which is equal to 4(a2 + b2 + c2 − ab − bc − ca)
Multiplying and dividing the expression by 2,
= 8(a2 + b2 + c2 − ab − bc – ca) / 2
= (2a2 + 2b2 + 2c2 − 2ab − 2bc − 2ca) 2
= (a2 − 2ab + b2 + b2 − 2bc + c2 + c2 − 2ca + a2) 2
= [(a − b)2 + (b − c)2 + (c − a)2] 2
from here we can say that the discriminant is non negative so the values of the roots of equation is always real.
Multiplying and dividing the expression by 2,
= 8(a2 + b2 + c2 − ab − bc – ca) / 2
= (2a2 + 2b2 + 2c2 − 2ab − 2bc − 2ca) 2
= (a2 − 2ab + b2 + b2 − 2bc + c2 + c2 − 2ca + a2) 2
= [(a − b)2 + (b − c)2 + (c − a)2] 2
from here we can say that the discriminant is non negative so the values of the roots of equation is always real.
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