If  roots of x2−(a−3)x+a=0  are such that at least one of the roots of greater than 2, then

The given equation is x2−(a−3)x+a=0 Let α,β  are the roots of the given equationHere a=1,b=−(a−3),c=aThe dicriminant is D≥0   ⇒ (a−3)2−4a≥0  ⇒a2−10a+9≥0⇒a≤1    or  a≥9If both roots are less than or equal to 2, thenf(2)≥0, And sum of the roots α+β≤4⇒    a−3≤4    i.e., a≤7 ∴    Values  of a such that at least one root is greater than 2 are given by(−∞, 1]∪[9,  ∞)−(−∞,  7]=[9,  ∞)