Question:
If the equation
\[
2x^2-5x+k=0
\]
has equal roots, then the value of \(k\) is
If the equation
\[
2x^2-5x+k=0
\]
has equal roots, then the value of \(k\) is
Show Hint
For equal roots, immediately use
\[
D=0.
\]
This is the fastest method and avoids unnecessary factorization.
Updated On: Jun 10, 2026
- \(\dfrac{25}{8}\)
- \(\dfrac{8}{25}\)
- \(\dfrac{25}{4}\)
- \(\dfrac{5}{2}\)
Show Solution
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The Correct Option is A
Solution and Explanation
Concept:
A quadratic equation
\[
ax^2+bx+c=0
\]
has equal roots if and only if its discriminant is zero.
The discriminant is
\[
D=b^2-4ac.
\]
Therefore, for equal roots,
\[
D=0.
\]
Step 1: Identify the coefficients Comparing \[ 2x^2-5x+k=0 \] with \[ ax^2+bx+c=0, \] we obtain \[ a=2,\qquad b=-5,\qquad c=k. \]
Step 2: Apply the equal roots condition \[ b^2-4ac=0. \] Substituting, \[ (-5)^2-4(2)(k)=0. \] \[ 25-8k=0. \] \[ 8k=25. \] \[ k=\frac{25}{8}. \] Hence, \[ \boxed{\frac{25}{8}}. \]
Step 1: Identify the coefficients Comparing \[ 2x^2-5x+k=0 \] with \[ ax^2+bx+c=0, \] we obtain \[ a=2,\qquad b=-5,\qquad c=k. \]
Step 2: Apply the equal roots condition \[ b^2-4ac=0. \] Substituting, \[ (-5)^2-4(2)(k)=0. \] \[ 25-8k=0. \] \[ 8k=25. \] \[ k=\frac{25}{8}. \] Hence, \[ \boxed{\frac{25}{8}}. \]
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