Question

If one of the zero of the quadratic polynomial 2x 2 + px +4 is 2 , then find the value of p.​

Answer 1

Answer:

-6

Step-by-step explanation:

2x² + px+4

2(2)² + 2p + 4 = 0

8 +2p+ 4 = 0

2p + 12 = 0

2p = -12

p= -6

therefore p= -6 is the right answer .

Answer 2

Explanation:

$\textsf{Given,}$

$2x^2 + px + 4 \:\textsf{has one of its roots as 2, meaning (x-2) is a factor of the polynomial.}$

$\textsf{We know that in a quadratic polynomial of form} \:\mathsf{ax^2 + bx + c, with\: roots\: \alpha \:and\: \beta, }$

$\mathsf{\alpha+ \beta =\frac{-b}{a}, \: \alpha\beta=\frac{c}{a}, \:meaning}$

$\mathsf{2\times \beta=\frac{4}{2}=2}$

∴ $\beta =1$

∴ $\mathsf{\alpha +\beta = \frac{-b}{a}}$

==> $\mathsf{2+1=\frac{-p}{2}}$

==> $\mathsf{\frac{-p}{2}=3}$  

∴ $\mathsf{-p=6, \:meaning \: p = -6}$

Answer: p = -6

$\textsf{I hope this helps. :D}$