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Shohini Sinha Ray Grade: Upto college level
        

The range of values of a for which roots of the quadratic equation x^2+x-3a+2=0 are of opposite sign is given by


a) a<1    


b) a>2


c) 1

d) 0

7 years ago

Answers : (1)

askIITIians Expert
21 Points
										












Your given equation is


x2 + x – 3a + 2 = 0


Since the roots are opposite in sign, so α x β is –ve                  (i)


Hence,


α x β = -3a + 2/1                 (ii)


Therefore, product of roots of the eq.


ax2 + bx + c = c/a


From equation (i) and (ii), we have


-3a + 2 < 0


-3a < -2


a > 2/3                           (i)


Also, discriminant D should be greater than 0 for roots to be real


Hence, 1 – 4 (-3a + 2) > 0


1 > 4(-3a + 2)


-12a + 8 < 1


-12a < -7


a > 7/12                          (ii)


Taking the intersection (i) and (ii) we have,


a > 2/3


Hence, the most appropriate option is (b) a > 2 , since a > 2/3


Then, a > 2.

7 years ago
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