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Question
If the roots of the equation x2+a2=8x+6a are real, then:
If the roots of the equation x2+a2=8x+6a are real, then:
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Solution
The correct option is D aϵ[−2,8]
The given equation can be written as
x2−8x+a2−6a=0
Since the roots of the above equation are real,
∴B2−4AC≥0⇒64−4(a2−6a)≥0
⇒a2−6a−16≤0
⇒(a+2)(a−8)≤0
⇒a ϵ [−2,8]
The given equation can be written as
x2−8x+a2−6a=0
Since the roots of the above equation are real,
∴B2−4AC≥0⇒64−4(a2−6a)≥0
⇒a2−6a−16≤0
⇒(a+2)(a−8)≤0
⇒a ϵ [−2,8]
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