Question

The least integer album value of a such that (a-3)x^2 +12x +(a+6)

Answer 1

Answer: the smallest integral value of a such that |x+a−3|+|x−2a|=|2x−a−3| is true ∀x∈R is

Step-by-step explanation:

the smallest integral value of a such that |x+a−3|+|x−2a|=|2x−a−3| is true ∀x∈R is

Answer 2

Step-by-step explanation:

Given The least integer album value of a such that (a-3)x^2 +12x +(a+6)

• So the quadratic equation is greater than 0 and so the coefficient of x^2 should be greater than 0.
• Now coefficient of x^2 is a – 3 > 0
• So a is greater than 3
• So the quadratic equation does not have any root.
• Therefore its determinant D < 0
• Now (a - 3)x^2 + 12x + a + 6
• b^2 – 4ac < 0
• (12)^2 – 4 (a – 3)(a + 6) < 0
• 144 – 4 (a – 3)(a + 6) < 0 taking 4 common we get
• 36 – (a – 3)(a + 6) < 0
• 36 – (a^2 + 3a – 18) < 0
• 36 – a^2 – 3a + 18 < 0
• a^2 – 3a + 54 > 0
• a(a + 9) – 6(a + 9) > 0
•    (a + 9)(a – 6) > 0
• So a = - 9, 6
• So we can write x ε (-ꝏ, -9) Ս (6, ꝏ)
• Therefore x ε (6,ꝏ)
• So the least integer will be 7

Reference link will be

https://brainly.in/question/40399061