MHT CET20239 May 2023Evening ShiftMathematicsStatisticsActual
If the mean and S.D. of the data 3,5,7, a , b are 5 and 2 respectively, then a and b are the roots of the equation
Options
- Ax^2-10 x+18=0
- B2 x^2-20 x+19=0
- Cx^2-10 x+19=0
- Dx^2-20 x+18=0
Correct answer
C. x^2-10 x+19=0
Step-by-step solution
Mean =5 ... [Given] aligned & Mean = _ i=1 ^ n x_i n & 5= 3+5+7+ a + b 5 & a + b =10 ... (i) aligned aligned & S.D. =2 ... [Given] & S.D. = x₁^2 n -( x )^2 & (2)^2= 3^2+5^2+7^2+ a ^2+ b ^2 5 -(5)^2 & 4= 83+ a ^2+ b ^2 5 -25 & a ^2+ b ^2=62 ... (ii) aligned ...[Given] Now, (i) a+b=10 Squaring both sides, we get array ll & (a+b)^2=100 & a^2+2 a b+b^2=100 & 38=2 a b ... [From (ii)] & a b=19 array Note that the required quadratic equation is expressed as aligned & x^2-( a + b ) x+ ab =0 & x^2-10 x+19=0 aligned