Question

Question below --- Easy, 20+ Points - Subject: Completing the square

Answer 1

Answer:

$p = \frac{3}{2},\: q = 9$

Step-by-step explanation:

$LHS = 4x^{2}+12x$

$= 4(x^{2}+3x)$

$=4[x^{2}+2\times x\times \big(\frac{3}{2}\big)]$

$=4[x^{2}+2\times x\times \big(\frac{3}{2}\big)+\left(\frac{3}{2}\right)^{2}-\left(\frac{3}{2}\right)^{2}]$

$=4[(x+\frac{3}{2})^{2}-\frac{9}{4}]$

$=4(x+\frac{3}{2})^{2}-4\times \frac{9}{4}$

$=4(x+\frac{3}{2})^{2}-9\:--(1)$

According to the problem given,

$4x^{2}+12 = 4(x+p)^{2}-q$

$4(x+\frac{3}{2})^{2}-9=4(x+p)^{2}-q\: [from \:(1) ]$

Compare both sides ,we get

$p = \frac{3}{2},\: q = 9$

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Answer 2

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