We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
347
1
avatar

If c is a constant such that 9x^2 + 10x + c is equal to the square of a binomial, then what is c?

 Jan 26, 2018
edited by Guest  Jan 26, 2018
 #1
avatar+22273 
+2

If c is a constant such that 9x^2 + 10x + c is equal to the square of a binomial, then what is c?

 

\(\begin{array}{|lrcll|} \hline &(9x^2+10x+c) &=& (3x+b)^2 \\ & &=& 9x^2+\underbrace{6b}_{=10}x+\underbrace{b^2}_{=c} \\\\ \hline (1) & 6b &=& 10 \\ & b &=& \frac53 \\\\ (2) & c &=& b^2 \\ & c &=& (\frac53)^2 \\ & c &=& \frac{25}{9} \\ \hline &\left(9x^2+10x+\dfrac{25}{9} \right) &=& \left(3x+\dfrac53 \right)^2 \\ \hline \end{array}\)

 

laugh

 Jan 26, 2018

22 Online Users

avatar
avatar