Let `a, b, c, p, q` be the real numbers. Suppose `alpha,beta` are the roots of the equation `x^2+2px+ q=0`. and `alpha,1/beta` are the roots of the equation `ax^2+2 bx+ c=0`, where `beta !in {-1,0,1}`. Statement I `(p^2-q) (b^2-ac)>=0` Statement 11 `b !in pa` or `c !in qa`.

Options

A. Statement -1 is true, Statement -2 is true, Statement -2 is a correct explanation for Statement-1
B. Statement -1 is true, Statement -2 is true, Statement -2 is not a correct explanation for Statement -1
C. Statement -1 is true, Statement -2 is false
D. Statement -1 is false, Statement -2 is true

Answer

B

Explanation

Suppose roots are imagnary then `beta=bar(alpha)`
and `1/(beta)=bar(alpha)`
`impliesbeta=-1/(beta)`[ not possible]
`implies` Roots are real `implies(p^(2)-q)(b^(2)-ac)ge0`
`implies` Statement `-1` is true.
`-(2b)/a=alpha+1/(beta)`
and `(alpha)/(beta)=c/a,alpha +beta=-2p, alpha beta=q`
If `beta=1`, then `alpha=q`
`impliesc=qa` [not possible]
Also `alpha+1=(-2b)/a`
`implies-2p=(-2b)/a`
`impliesb=ap` [not possible]
`implies` Statement `-2` is treu but it is not the correct explanation of Statment-1