Question

Find the least positive value of k for which the equation x² + kx + 4 = 0 has real roots.

Answer 1

SOLUTION :  

Given : x² + kx + 4 = 0

On comparing the given equation with ax² + bx + c = 0

Here, a = 1 , b = k  , c = 4

D(discriminant) = b² – 4ac

D = (k)² - 4 × 1 × 4

D = k² - 16  

D = ≥ 0 (Given : roots are real )

k² - 16 ≥ 0

k² ≥ 16

k ≥ √16  

k ≥ 4

k = 4

[Given : value of k is positive]

Hence, the least positive value of x² + kx + 4 = 0  is 4 .

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Answer 2

Heya !
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→Given Equation = x² + kx + 4 = 0

★ For an equation to have real roots , b² - 4ac ≥0

=> So let's calculate the discriminant ( D ) = b² - 4ac

• We have a = 1 , b = k , c = 4

=> D = k² - 4 × 1 × 4

=> D = k² - 16

★ Now we have , D ≥ 0

=> k² - 16 ≥ 0

=> k² ≥ 16

=> k ≥ 4 [ value of k is to be positive ]

=> As we needed the positive value ,.Hence avoiding the negative value , we have the least value as

★ K = 4 ✔

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