Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation

Let and be the roots of the equation x^2-5 x+5=0 . If b= + and t=x^2-4 x+3 b- 1 5 + 1 x^2-4 x+9 , x R then:

Options

Aminimum value of (b+t) is 8
Bmaximum value of _ 1 / 5 (t) is -1
Crange of y= ⁻¹ ( ₅ t ) is (0, 4 ]
Drange of y= ⁻¹ ( _ 1 / 5 (t) ) is [ 4 , )

Correct answer

C. range of y= ⁻¹ ( ₅ t ) is (0, 4 ]

Step-by-step solution

b= ^2+ ^2 = ( + )-2 = 25-10 5 =3 aligned & t=x^2-4 x+9- 1 5 + 1 x^2-4 x+9 & t=(x-2)^2+5- 1 5 + 1 (x-2)^2+5 & t_ min. =5 ( at x=2) aligned (1) Minimum value of b+t=3+5=8 (2) _ 1 / 5 5=-1 , maximum (3) aligned & y= ⁻¹ ( ₅ t ), t 5 & ₅ t [1, ) & ⁻¹ ( _t 5 ) (0, 4 ] aligned (4) aligned & y= ⁻¹ ( _ 1 / 5 (t) ) & _ 1 / 5 t (- ,-1] & ⁻¹ ( _ 1 / 5 (t) ) [ 3 4 , ) aligned

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