If x^{2}-x+a-3<0 for atleast one negative value of x, then the complet

1.	If x^{2}-x+a-3<0 for atleast one negative value of x, then the complete set of values of 'a are
Answer» The functionf(x) = x^2 -x + (a-3)is a quadratic polynomial . Its leading coeffcient is positive. f’’(x)>0so it isconcave upwards. The graph shifts up and down depending on varying theconstanta CASE 1: EXACTLY ONE ROOT NEGATIVE zero lies b/w roots. f(0)<0 a-3<0 a<3 CASE 2: BOTH ROOTS NEGATIVE As the abscissa of vertex is x= 1/2 which is positive. so this case is ruled out. Hencea belongs from -∞ to 3 The limiting case when a=3

If x^{2}-x+a-3<0 for atleast one negative value of x, then the complete set of values of 'a are

Answer»

The functionf(x) = x^2 -x + (a-3)is a quadratic polynomial .

Its leading coeffcient is positive.

f’’(x)>0so it isconcave upwards.

The graph shifts up and down depending on varying theconstanta

CASE 1: EXACTLY ONE ROOT NEGATIVE

zero lies b/w roots.

f(0)<0

a-3<0

a<3

CASE 2: BOTH ROOTS NEGATIVE

As the abscissa of vertex is x= 1/2 which is positive.

so this case is ruled out.

Hencea belongs from -∞ to 3

The limiting case when a=3