यदि बहुपद x 3 – 3x 2 + x + 1 के शून्यक (a – b), a, (a + b), हों तो 'a' और 'b' ज्ञात कीजिएl - Wired Faculty

बहुपद

Question

यदि बहुपद x³ – 3x²+ x + 1 के शून्यक (a – b), a, (a + b), हों तो 'a' और 'b' ज्ञात कीजिएl

Solution

क्योंकि a – b, a और a + b बहुपद के शून्यक है

rightwards double arrow

space space space space space straight a space minus space straight b space plus space straight a space plus space straight a space plus space straight b space equals space minus space fraction numerator straight x squared space क े space ग ु ण ां क over denominator straight x cubed space क े space ग ु ण ां क end fraction

equals space fraction numerator negative space left parenthesis space minus space 3 space right parenthesis over denominator 1 end fraction

rightwards double arrow

3 straight a space equals space 3 space rightwards double arrow space straight a space equals space 1

rightwards double arrow

( a - b ) a ( a + b ) =

negative space fraction numerator स ् थ ि र ां क over denominator straight x cubed space क े space ग ु ण ां क end fraction

equals space minus space 1 over 1

rightwards double arrow

straight a space left parenthesis space straight a squared space minus space straight b squared space right parenthesis space equals space minus 1 space rightwards double arrow space 1 space minus space straight b squared space equals space minus 1

rightwards double arrow

straight b squared space equals space 2 space rightwards double arrow space space straight b space equals space plus-or-minus space square root of 2

अत:,

straight a space equals space 1 comma space space straight b space equals space plus-or-minus space square root of 2

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