Two zeroes of cubic polynomial ax3 + 3x2 – bx – 6 are –1 and –2. Find the third zero and value of a and b.

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Balaji Puppala

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Let P(x)=ax3+3x2-bx-6 since -1,-2 are zeroes of the given polynomial, we have P(-1)=0,P(-2)=0 So, -a+b-3=0 and -4a+b+3=0 By solving, we get a=2, b=5 So given polynomial is 2x3+3x2-5x-6 Compare given polynomial with ax3+bx2+cx+d We get a=2, b=3, c=-5, d=-6 and zeroes are p=-1,q=-2,r We have P+q+r=-3/2,...
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Let P(x)=ax3+3x2-bx-6 since -1,-2 are zeroes of the given polynomial, we have P(-1)=0,P(-2)=0 So, -a+b-3=0 and -4a+b+3=0 By solving, we get a=2, b=5 So given polynomial is 2x3+3x2-5x-6 Compare given polynomial with ax3+bx2+cx+d We get a=2, b=3, c=-5, d=-6 and zeroes are p=-1,q=-2,r We have P+q+r=-3/2, p×q×r=6/2=3 So, -3+r=-3/2⇒r=3/2 Another zeroes of the polynomial is 3/2 read less
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