Question

If one zero of a polynomial 2x²+p x +4 is 2 , then the value of p is

Answer 1

Answer:

given alpha=2

then sum of roots (alpha+beta)=-b/a

product of root alpha*beta=c/a

alpha*beta=4/2

2*beta=2

beta=1

alpha+beta=-p/2

2+1=-p/2

3*2=-p

p=-6 ans..

Answer 2

Answer:

• The value of p is -6.

Given:

• One of the zero of a polynomial 2x² + px + 4 is 2.

To find:

• The value of p.

Solution:

⠀⠀⠀⠀f (x) = 2x² + px + 4 ; f (x) = 0

⠀⠀>> f (2) = 2(2)² + 2p + 4

⠀⠀>> 2(4) + 2p + 4 = 0

⠀⠀>> 8 + 2p + 4 = 0

⠀⠀>> 2p = -12

⠀⠀>> p = -6

Therefore, the value of p is -6.

______________________________

Verification:

⠀⠀⠀⠀f (x) = 2x² + px + 4

Substitute p = -6

⠀⠀>> 2x² - 6x + 4 = 0

⠀⠀>> x² - 3x + 2 = 0

⠀⠀>> x² - x - 2x + 2 = 0

⠀⠀>> x (x - 1) - 2 (x - 1) = 0

⠀⠀>> (x - 1) (x - 2) = 0

⠀⠀>> x = 1 or 2

Here, one of the zero of the polynomial is 2.

Hence, verified.

________________________________

Extra information:

• $\sf{Sum \ of \ zeroes=\dfrac{-b}{a}}$

• $\sf{Product \ of \ zeroes =\dfrac{c}{a}}$