# Let #h(x)=12x+x^2#, how do you find a such that h(a)=-27?

##### 2 Answers

Nov 14, 2016

#### Explanation:

Nov 14, 2016

#### Explanation:

Express h(x) in terms of a.

That is

#h(color(red)(a))=12color(red)(a)+(color(red)(a))^2=12a+a^2#

#h(a)=-27" and " h(a)=12a+a^2#

#"solve " 12a+a^2=-27" to find a"# since this is a quadratic function, equate to zero.

#rArra^2+12a+27=0# using the a-c method, we require the product of factors of 27 that also sum to + 12. These are +3 and +9.

#rArr(a+3)(a+9)=0# solve :

#a+3=0rArra=-3# solve :

#a+9=0rArra=-9# Check :

#a=-3rArr12xx(-3)+(-3)^2=-36+9=-27color(white)(x)#

#a=-9rArr12xx(-9)+(-9)^2=-108+81=-27#

#rArra=-3,a=-9" are the solutions"#