Let `a ,b , c ,p ,q` be real numbers. Suppose `alpha,beta` are the roots of the equation `x^2+2p x+q=0,alphaa n d1//beta` are the roots of the equation`a x^2+2b x+c=0,w h e r ebeta^2 !in {-1,0,1}dot` Statement 1: `(p^2-q)(b^2-a c)geq0` Statement 2: `b!=p aorc!=q a`

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