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CBSE Class 10 Standard Math 2025 All Sets Solved Paper

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Question : 14 of 20
Marks: +1, -0
If x2+bx+b=0x^2 + bx + b = 0 has two real and distinct roots, then the value of b can be
Solution:  
x2+bx+b=0x^2+b x+b=0
Here,
a = 1
b = b
c = b
D=b24ac\therefore D = b^2 - 4 a c
=b24×1×b= b^2 - 4 \times 1 \times b
=b24b= b^2 - 4 b
For the quadratic equation to have "two real and distinct roots".
D >0
b24b>0b^2 - 4 b > 0
b(b4)>0b(b-4) > 0
From the given options:-
(A) 0
b = 0
b(b4)0b(b-4) \ge 0
incorrect
(B) 4
b = 4
b(b4)>0b(b-4) > 0
4(44)>04(4-4) > 0
4×0>04 \times 0 > 0
0 > 0
incorrect
(C) 3
b = 3
b(b - 4) > 0
3(34)>03(3-4) > 0
3×(1)>03 \times (-1) > 0
-3 > 0
incorrect.
(D) -3
b = -3
b(b4)>0b(b-4) > 0
3(34)>0-3(-3-4) > 0
3(7)>0-3(-7) > 0
21 > 0
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