Complex Numbers And Quadratic Equations question 20
Question: . If $ x $ is real, then the value of $ x^{2}-6x+13 $ will not be less than [RPET 1986]
Options:
A) 4
B) 6
C) 7
D) 8
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ y=x^{2}-6x+13\Rightarrow x^{2}-6x+13-y=0 $ Its discriminant $ D\ge 0\Rightarrow 36-4(13-y)\ge 0 $
Þ $ 36-52+4y\ge 0\Rightarrow 4y\ge 16\Rightarrow y\ge 4 $ Hence y is not less than 4. Aliter: $ x^{2}-6x+13={{(x-3)}^{2}}+4 $ Obviously the minimum value is 4.
BETA
