Question

Q.3. Find cubic polynomial p(x) = x3 + 2x2 – 3x. Also verify the
relationship between the zeros and coefficients of p(x). (3)​

Answer 1

Answer:

Step-by-step explanation:

plz mark me brainlist

Answer 2

Given :  p(x) = x³ + 2x² - 3x

To Find : Zeroes and verify relationship between coefficients

Solution:

p(x) = x³ + 2x² - 3x

x³ + 2x² - 3x  = 0

=> x(x² + 2x - 3) = 0

=> x(x² + 3x - x - 3) = 0

=> x(x (x + 3) - 1(x + 3) ) = 0

=> x(x - 1) (x + 3) = 0

=> Zeroes are

0 , 1  - 3

P(x) = ax³ + bx² + cx + d

p(x) = x³ + 2x² - 3x

=> a = 1  , b = 2 , c = - 3 , d =  0

Sum of zeroes = - b/a   = - 2/1 = - 2

Sum of zeroes = 0 + 1 - 3 = - 2

-2 = - 2  verified

Sum of product of zeroes 2 taken  at time = c/a = -3/1 = - 3

0(1) + 0(-3) + 1(-3) = -3

-3 = - 3  verified

product of zeroes 3 taken  at time = -d/a = -0/1 = 0

0(1)(-3) = 0

0 = 0  verified

Zeroes are 0 ,1 - 3

relationship between the zeros and coefficients of p(x)  verified

Learn More:

Each coefficient in the equation ax2 + bx + c = 0 is determined by ...

https://brainly.in/question/6073448

If the sum of the product of deviations of x and y series from their ...

https://brainly.in/question/25861692