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$(x+4)(2x-a)=0$ if the equation has the solutions of $x=4$ and $x=(-4)$ what is the value of $a$ ?

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Solve quadratic inequalities

Full solution

Q.

(x+4)(2x-a)=0

if the equation has the solutions of

x=4

and

x=(-4)

what is the value of

a

?

Substitute $x=4$ : Since the equation $(x+4)(2x-a)=0$ has the solutions $x=4$ and $x=-4$ , we can use these solutions to find the value of $a$ .
Isolate $(8-a)$ : First, let's substitute $x=4$ into the equation $(x+4)(2x-a)=0$ . This gives us $(4+4)(2\cdot 4-a)=0$ , which simplifies to $8(8-a)=0$ .
Solve for $a$ : Since $8(8-a)=0$ , we can divide both sides by $8$ to isolate $(8-a)$ . This gives us $8-a=0$ .
Check $x=-4$ : Solving the equation $8-a=0$ for $a$ gives us $a=8$ .
Confirm $a=8$ : Now, let's check the second solution $x=-4$ to ensure it is consistent with the value of $a$ we found. $\newline$ Substitute $x=-4$ into the equation $(x+4)(2x-a)=0$ . $\newline$ This gives us $(-4+4)(2*(-4)-a)=0$ , which simplifies to $0*(a-8)=0$ .
Confirm $a=8$ : Now, let's check the second solution $x=-4$ to ensure it is consistent with the value of $a$ we found. $\newline$ Substitute $x=-4$ into the equation $(x+4)(2x-a)=0$ . $\newline$ This gives us $(-4+4)(2*(-4)-a)=0$ , which simplifies to $0*(a-8)=0$ .Since $0*(a-8)=0$ is true for any value of $a$ , it confirms that our value of $a=8$ is correct and does not contradict the second solution $x=-4$ .

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