Question

S(x) = px² +(p-2)x +2. If 2 is the zero of this polynomial,what is the value of p *

Answer 1

Answer:

$\red{\boxed{\rm Solution}}$

Given,

S(x) = px² + (p - 2)x + 2

We know that to find zero of a polynomial p(x) we have to actually find the x when p(x) = 0

We know that to find zero of a polynomial p(x) we have to actually find the x when p(x) = 0Given that zero of the polynomial S(x) = 2, that means when S(x) = 0 the value of x = 2

p(2)² + (p - 2)2 + 2 = 0

4p + 2p - 4 + 2 = 0

6p - 2 = 0

6p = 2

p = 2/6

p = 1/3

Verification:-

x²/3 + (1/3 - 2)x + 2 = 0

x²/3 + [(1 - 6)/3]x + 2= 0

x²/3 - 5x/3 + 2 = 0

(x² - 5x + 6)/3 = 0

x² - 5x + 6 = 0

x² - 2x - 3x + 6 = 0

x(x - 2) - 3(x - 2) = 0

(x - 2)(x - 3) = 0

x - 2 = 0 , x - 3 = 0

x = 2 , x = 3

Here we got two zeros of the polynomial which are x = 2 and x = 3

Now let's check the value of p is 1/3 even when x = 3 as the zero of the polynomial.

p(3)² + (p - 2)3 + 2 = 0

9p + 3p - 6 + 2 = 0

12p - 4 = 0

12p = 4

p = 4/12

p = 1/3

Hence in both the cases we got p = 1/3

Therefore,

$\boxed{\rm p \: = \: \frac{1}{3} }$

Answer 2

Answer:

if 2 is the Zero of the polynomial then,

s(2)=p(2)²+(p-2) 2+2

p(2)=4p²+2p-2

p(2) will be equal to Zero so,

4p²+2p-2=0 by solving this equation we get,

P=1/2 or -1