Question

What is the possible values of b when the difference between the roots of the equation
x? + bx +1=0 is less than 12.
(a) (4.00
(b) (-00, -4 )
(c) |–4,4
(d) (-4,4)
Answer
А
B
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Answer 1

Given info : the difference of roots of quadratic equation x² + bx + 1 is less than √12 (you did wrong in typing).

To find : the possible value of b.

Solution : let α and β are the roots of given quadratic. Where α > β

Here given, α - β < √12

⇒(α - β)² < 12 [ if we assume α - β is positive ]

⇒(α + β)² - 4αβ < 12

From quadratic equation, x² + bx + 1 = 0

α + β = -b and αβ = 1

Now, (-b)² - 4 × 1 < 12

⇒(b² - 16) < 0

⇒-4 < b < 4

Therefore the possible value of b is (-4, 4)

Answer 2

Answer:-

Given info :

the difference of roots of quadratic equation x² + bx + 1 is less than √12 (you did wrong in typing).

To find : the possible value of b.

Solution :

let α and β are the roots of given quadratic. Where α > β

Here given, α - β < √12

⇒(α - β)² < 12 [ if we assume α - β is positive ]

⇒(α + β)² - 4αβ < 12

From quadratic equation, x² + bx + 1 = 0

α + β = -b and αβ = 1

Now, (-b)² - 4 × 1 < 12

⇒(b² - 16) < 0

⇒-4 < b < 4

Therefore the possible value of b is (-4, 4)

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