Question

If the value of a quadratic polynomial p(x) is 0 only
at x=-1 and p(-2) = 2, then the value of p(2) is
(NTSE- Stage 2, 2016)​

Answer 1

Consider the quadratic equation as:
p(x) = x² - bx + c = 0
at x=(-1), p(x) = 0, that is p(-1) = 0
p(-1) = (-1)² - b(-1) + c = 0
1 + b + c = 0 __________(1)

p(-2) = (-2)² - b(-2) + c = 0
4 + 2b + c =0 _________(2)

Now, Solve these 2 equation
from equation (1):
c = -(b +1)

put this "c" in equation (2):
4 + 2b + (-(b +1)) = 0
4 + 2b - b - 1 = 0
4 + b - 1 = 0
b = -3
and c = -(-3 + 1) = -(-2) = 2

So the quadratic equation is:
x² - (-3)x + 2 = 0
x² + 3x + 2 = 0

Thankyou!!!

Answer 2

Hola mate

Here is you answer -

 

Consider the quadratic equation as:

p(x) = x² - bx + c = 0

at x=(-1), p(x) = 0, that is p(-1) = 0

p(-1) = (-1)² - b(-1) + c = 0

1 + b + c = 0 __________(1)

p(-2) = (-2)² - b(-2) + c = 0

4 + 2b + c =0 _________(2)

 

Now, Solve these 2 equation

from equation (1):

c = -(b +1)

 put this "c" in equation (2):

4 + 2b + (-(b +1)) = 0

4 + 2b - b - 1 = 0

4 + b - 1 = 0

b = -3

and c = -(-3 + 1) = -(-2) = 2

So the quadratic equation is:

x² - (-3)x + 2 = 0

x² + 3x + 2 = 0

Hope it helps you!