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What value of c makes x2 6x c a perfect square trinomial? c = If x2 6x c = (x d)2, then d =.

Sagot :

[tex]\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^2 \pm \stackrel{\stackrel{2\sqrt{x^2}\sqrt{c^2}}{\downarrow }}{6x} +c^2~\hspace{10em}6x=2\sqrt{x^2}\sqrt{c^2}\implies 6x=2xc \\\\\\ \cfrac{6x}{2x}=c\implies 3=c\implies 9=c^2~\hfill \boxed{(x\pm 3)^2}[/tex]

ashishdwivedilVT

c=9 makes the given expression a perfect square trinomial.

The given expression is:

[tex]x^{2} +6x+c[/tex]

We can rewrite it as:

[tex]x^{2} +2*x*3 + c[/tex].....(1)

What is the expansion of  [tex](a+b)^2[/tex]?

The expansion of [tex](a+b)^2[/tex] is [tex]a^{2} +2ab+b^{2}[/tex]

Comparing (1) with [tex]a^{2} +2ab+b^{2}[/tex]

We get

a=x

b=3

c=b²

So, c=3² =9.

So, c=9 makes the given expression a perfect square trinomial.

Hence,  c=9 makes the given expression a perfect square trinomial.

To get more about polynomials visit:

https://brainly.com/question/2833285

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