If one of the zeros of of the quadratic equation 2 X square + bx + 4 is 2. Find the other zeros and also find the value of p
Answers
Answer:
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+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