Question

if one of the zeros of the quadratic polynomial 2x2+px+ 4 is 2 find the zero also find the value of p

Answer 1

$\textbf{ANSWER:}$

The zero of a quadratic polynomial is referred to the value which when put in the equation, results 0.

The zero of the quadratic polynomial:
$2 {x}^{2} + px + 4 \: \: \: \: \: \: ...(1)$
Is 2. ... (2)

Putting (2) in (1):
$2( {2})^{2} + 2p + 4 = 0\\ \\ = > 8 + 2p = ( - 4) \\ \\ = > 2p = ( - 4 - 8) \\ \\ = > 2p = ( - 12) \\ \\ = > p = \frac{ (- 12)}{2} \\ \\ = > p = ( - 6)$

You can even check your answer by putting (2) in (1) and the value of p as (-6).

#BeBrainly

Answer 2

$<b >Hey here is your answer$

p(x) = 2x^2 + px + 4

It is given that 2 is the zeros if this polynomial.

so,

putting x = 2 in p(x)

p(2) = 2

By factor theorem :-

p(2) = 2(2)² + p(2) + 4
= 2×4 + 2p + 4 = 0
= 8 + 2p + 4 = 0
= 12 + 2p = 0
= 2p = 0 - 12
= p = -12/2 = (-6)

So, P = (-6) answer

NOW,

putting p = (-6) in p(x)

= 2x^2 + (-6)x + 4
= 2x^2 - 6x + 4

By Factorisation :-

= 2x^2 - 6x + 4
= 2x^2 - 4x - 2x + 4
= 2x (x - 2) - 2 (x - 2)
= (x - 2)(2x - 2)

NOW,

Zeros of (x - 2)(2x - 2)

(x - 2) = 0
= x = 2

second zeros of (x - 2)(2x - 2)

2x - 2 = 0
2x = 2
x = 2/2 = 1

hope this helps you

### BE BRAINLY ###