Question

if '2' is one of the zeroes of the polynomial then find other zeroes​

Answer 1

Answer:

Value of p is -

Step-by-step explanation:

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+cax

2

+bx+c

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

2

+px+4=0 is −

a

b

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

2

+px+4=0 is

a

c

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

First let us find product of roots which is

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

αβ=

a

c

=

2

4

=2

αβ=2

2b=2

b=1

Now, sum of roots,

\begin{lgathered}\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}\end{lgathered}

(α+β)=−

a

b

=−

2

p

2+1=−

2

p

3=−

2

p

p=−6

HOPE IT WILL HELP

Answer 2

You need to mention the polynomial mate !

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