Question

If one of the zeroes of the polynomial 2x 2 + px 4 = 0 is 2, find the other root. Also find the value of p.

Answer 1

Value of p is -6

Solution:

To find value of p let us find the roots of the equation by finding the product and sum of equation in form of $ax^2+bx+c$

Sum of roots of quadratic equation of $2 x^{2}+p x+4=0 \text { is }-\frac{b}{a}$

In addition, product of roots of equation $2 x^{2}+p x+4=0 \text { is } \frac{c}{a}$

Sum of roots = $(\alpha+\beta), \text { with } \alpha=2, \beta=b$

First let us find product of roots which is              

$\begin{array}{l}{\alpha \beta=\frac{c}{a}=\frac{4}{2}=2} \\ \\{\alpha \beta=2} \\ \\{2 b=2} \\ \\{b=1}\end{array}$

Now, sum of roots,

$\begin{array}{l}{(\alpha+\beta)=-\frac{b}{a}=-\frac{p}{2}} \\ \\{2+1=-\frac{p}{2}} \\ \\{3=-\frac{p}{2}} \\ \\ \bold{{p=-6}} \end{array}$

Answer 2

Answer:

Value of p = -6,

and

Other root = 1

Step-by-step explanation:

Given quadratic equation

2x²+px+4 = 0 ---(1)

and

One root (m) = 2 /* given

Let the second root = n

i ) Substitute m=2 in equation (1), we get

2(2)²+p×2 +4 =0

=> 8+2p+4=0

=> 12+2p=0

=> 2p = -12

Divide each term by 2, we get

=> p = -6

ii ) Now,

Compare 2x²+px+4 =0 with

ax²+bx+c=0, we get

a = 2 , b = p , c = 4

$Sum\: of\: the\: roots =\frac{-b}{a}$

$\implies m+n=\frac{-(-6)}{2}$

$\implies 2+n=\frac{6}{2}$

$\implies 2+n=3$

$\implies n=3-2$

$\implies n=1$

Therefore,

Value of p = -6

and

Other root = 1

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