Question

If the roots of the equation x^2+2(a-3)x+9=0 lies between -6 and 1, find the integral part of a.
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Answer 1

Answer:

$a∈(−∞,4−3).$

Step-by-step explanation:

f(x)=x

2

+2(a−3)x+9=0

α<6<β

⇒f(6)<0

⇒6

2

+2(a−3)6+9<0

⇒36+12(a−3)+9<0

⇒12a+9<0

⇒a<

4

−3

⇒a∈(−∞,

4

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$a∈(−∞,4−3).$