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The Values of K for Which the Quadratic Equation 16 X 2 + 4 K X + 9 = 0 Has Real and Equal Roots Are - CBSE Class 10 - Mathematics

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Question

The values of k for which the quadratic equation  \[16 x^2 + 4kx + 9 = 0\]  has real and equal roots are

 
  • \[6, - \frac{1}{6}\]

  • 36, −36

  •  6, −6

  • \[\frac{3}{4}, - \frac{3}{4}\]

Solution

The given quadratic equation  \[16 x^2 + 4kx + 9 = 0\]

has equal roots.

Here, 

\[a = 16, b = 4k \text { and } c = 9\] .

As we know that 

\[D = b^2 - 4ac\]
Putting the values of  \[a = 16, b = 4k \text { and } c = 9\].

\[D = \left( 4k \right)^2 - 4\left( 16 \right)\left( 9 \right)\]

\[ = 16 k^2 - 576\]

The given equation will have real and equal roots, if D = 0

Thus, 

\[16 k^2 - 576 = 0\]

\[\Rightarrow k^2 - 36 = 0\]

\[ \Rightarrow (k + 6)(k - 6) = 0\]

\[ \Rightarrow k + 6 = 0 \text { or } k - 6 = 0\]

\[ \Rightarrow k = - 6 \text { or } k = 6\]

Therefore, the value of k is 6, −6.

  Is there an error in this question or solution?

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Solution The Values of K for Which the Quadratic Equation 16 X 2 + 4 K X + 9 = 0 Has Real and Equal Roots Are Concept: Solutions of Quadratic Equations by Factorization.
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