Question

verify that 1,-1 and -3 are the zeroes of the cubic polynomial x³+3x²-3 and check the relationship between zeroes and coefficients.​

Answer 1

Answer:

Let given cubic polynomial be

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

= -1 + 3 + 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 given

cubic polynomial p(x).

Compare the coefficients of given

cubic polynomial x³+3x²-x-3 with

ax³+bx²+cx+d , we 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

Answer 2

Answer:

Let given cubic polynomial be

Let given cubic polynomial bep(x) = x³ + 3x² - x - 3

Let given cubic polynomial bep(x) = x³ + 3x² - x - 3i ) If x = 1 , then

p(1) = 1³ + 3(1)² - 1 - 3 = 1 + 3 - 1 - 3 = 0

p(1) = 1³ + 3(1)² - 1 - 3 = 1 + 3 - 1 - 3 = 0ii ) If x = -1 , then

cubic polynomial p(x)Compare the coefficients of given

cubic polynomial x³+3x²-x-3 with

ax³+bx²+cx+d , we get

a = 1 , b = 3 , c = -1 , d = -3

a = 1 , b = 3 , c = -1 , d = -3Let the zeroes of the cubic polynomial

p(x) are p = 1 , q = -1 , r = -3

p(x) are p = 1 , q = -1 , r = -3Now ,

p(x) are p = 1 , q = -1 , r = -3Now ,p + q + r = 1 - 1 - 3 = -3 = -b/a

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

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

pq + qr + rp = 1(-1)+(-1)(-3)+(-3)1= -1 + 3 - 3= -1 = c/a

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

Step-by-step explanation:

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