Question

this polynomial chapter 10th class plz help me friends ​

Answer 1

Let given cubic polynomial be ,

p(x) = x³ + 3x² - x - 3

p(x) = x³ + 3x² - x - 3 i ) If x = 1 , then

p(1) = 1³ + 3(1)² - 1 - 3

= 1 + 3 - 1 - 3

= 0

ii ) If x = -1 ,

then

p(-1) = ( -1 )³ + 3( -1 )² - ( -1 ) - 3

= 0

iii ) If x = -3 , then

p(-3) = (-3)³ + 3(-3)²-(-3)-3

= -27 + 27 + 3 - 3

= 0

Therefore ,

p(1) = p(-1) = p(-3) = 0.

So, 1 , -1 , -3 are zeroes of the givencubic polynomial p(x).

Compare the coefficients of given cubic polynomial x³+3x²-x-3 with ax³+bx²+cx+d ,

we get

get a = 1 , b = 3 ,

c = -1 , d = -3

Let the zeroes of the cubic polynomial p(x) are p = 1 ,

q = -1 , r = -3

Now , p + q + r = 1 - 1 - 3 = -3 = -b/a

pq + qr + rp = 1(-1)+(-1)(-3)+(-3)1

= -1 + 3 - 3= -1 = c/a

pqr = 1(-1)(-3) = 3 = -d/a

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