For any real value of k, the roots of the quadratic equation x2 + kx - 9 = 0 are : 1. real and equal 2. imaginary 3. real and unequal 4. none of these

D = b2 - 4ac Substituting values we get : D = k2 - 4 × 1 x (-9) = k2 + 36 For any real value of k, k2 + 36 is a positive number. ∴ D 0 ∴ Roots are real and unequal. Hence, Option 3 is the correct option.

Mathematics

For any real value of k, the roots of the quadratic equation x² + kx - 9 = 0 are :
real and equal
imaginary
real and unequal
none of these

Quadratic Equations

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Answer

D = b² - 4ac

Substituting values we get :

D = k² - 4 × 1 x (-9)

= k² + 36

For any real value of k, k² + 36 is a positive number.

∴ D > 0

∴ Roots are real and unequal.

Hence, Option 3 is the correct option.

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Mathematics

For any real value of k, the roots of the quadratic equation x² + kx - 9 = 0 are :
real and equal
imaginary
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none of these

Quadratic Equations

Answer

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