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my question is of quadratic equation . if x 2 +(a-b)x+(1-a-b)=0 where a, b belongs to real number then find the values of “a” which equation unequal real roots for all values of “b”?

my question is of quadratic equation . if x2+(a-b)x+(1-a-b)=0 where a, b belongs to real number then find the values of “a” which equation unequal real roots for all values of “b”?

Grade:11

1 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
7 years ago
Hi student

Discriminant of above equation is – (a-b)2 – 4(1-a-b)
For unequal roots D>0
=> a2 + b2 -2ab – 4 + 4a + 4b > 0
b2 -2b(a -2) + a2 -4 +4a > 0

now this is also quadratic in b and it is given this should hold for all b
which means D for this equation should be <0 So that graph will always be above x axis and inequality will always be true
(-2(a-2))2 – 4(a2 -4 +4a) <0
a2 + 4 -4a -a2 +4 -4a < 0
-8a +8<0
a>1

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