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&lt;1 b) a&gt;2 c) 1&lt;a&lt;2 d) 0&lt;a&lt;infinity

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

9 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.