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If sin alpha and cos alpha are roots of...

If `sin alpha and cos alpha` are roots of the equation `px^2 + qx+r=0` then :

A

`p^(2) +q^(2) -2pr =0`

B

`(p+r)^(2) =q^(2) +r^(2)`

C

`p^(2)-q^(2) + 2pr=0`

D

`(p+r)^(2)=q^(2) -r^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Since , `sin prop and cos prop ` are the roots of the equation
` px^(2) +qx =r=0`
` sin prop + cos prop = - q/p`
` and p sin^(2) prop + q sin prop +r =0`
` p cos^(2) prop + q cos prop + r =0`
Adding Eqs (i) and (ii) we get
` p (sin^(2) prop + cos^(2) prop) +q (sin prop + cos prop) +2r=0`
` Rightarrow p + q (-q/p) + 2r =0`
` Rightarrow p^(2) -q^(2) +2rp =0`
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Knowledge Check

  • If sin alpha and cos alpha are the roots of the equation px^2+qx+r=0 , then

    A
    `p^2+q^2-2pr=0`
    B
    `p^2-q^2+2pr=0`
    C
    `p^2-q^2-2pr=0`
    D
    `p^2+q^2+2qr=0`

  • If sin alpha and cos alpha are the roots of the equation px^2+qx+r=0 , then

    A
    `p^2+q^2-2pr=0`
    B
    `p^2-q^2+2pr=0`
    C
    `p^2-q^2-2pr=0`
    D
    `p^2+q^2+2qr=0`

  • If sin alpha and cos alpha are the roots of the equation px^(2)+qx+r=0 , then

    A
    `p^(2)-q^(2)+2pr =0`
    B
    `( p+r)^(2)=q^(2)-r^(2)`
    C
    `p^(2)+q^(2)-2pr=0`
    D
    `(p-r)^(2)=q^(2)+r^(2)`

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