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CBSE Class 10 Standard Math 2026 All Sets Solved Paper

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Question : 11 of 20
Marks: +1, -0
If roots of the quadratic equation x2−k3x+2=0x^2 - k\sqrt{3}x + 2 = 0 are real and equal, then value of k is
Solution:  
For a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 to have real and equal roots, its discriminant must be zero.
Discriminant (D) = b2−4ac=0.b^2 - 4ac = 0.
Here, a=1,b=−k3,c=2a = 1, b = -k\sqrt{3}, c = 2
(−k3)2−4(1)(2)=0(-k\sqrt{3})^2 - 4(1)(2) = 0
3k2−8=03k^2 - 8 = 0
3k2=83k^2 = 8
k2=83k^2 = \frac{8}{3}
k=±83k = \pm \sqrt{\frac{8}{3}}
The value of k is 83\sqrt{\frac{8}{3}}.
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