Question

Find the value c that will make 9x^2 +30x+c a perfect square trinomial

Answer 1

Answer:

$c = 25$

Step-by-step explanation:

Given :-

• A quadratic equation is given to us.
• The equation is 9x² + 30x + c .

And we need to find out the value of c for which the given trinomial is a perfect square. On looking at the given expression all the terms are having positive signs before them .So we can rewrite it on the basis of ,

Identity :-

$\implies (a+b)^2=a^2+b^2+2ab$

Let's try to set the equation on this Identity .

The firsr term is 9x² . We can write it as ,

$\implies 9x^2=(3x)^2$

Hence the middle term here should contain 3 and 2 as their factors. Let's Break the middle term .

$\implies 30x = 2.3x.5$

Therefore in order to make the whole expression as perfect square 5² must be replaced by c . The expression would become ,

$\implies 9x^2+30x + 5^2 \\\\\implies (3x)^2+2.3x.5 +5^2\\\\\implies (3x+5)^2$

Hence the value of c should be 25 .

Answer 2

C = 25 you just multiply step by step exactly how it shows it on the problem/how u wrote it