The of roots $A x^{2} + B x + C = 0$ are r and s. For the roots of $x^{2} + p x + q = 0$ to be $r^{2}$ and $s^{2}$ , p must equal:

\frac{B^{2} - 4 A C}{A^{2}}

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\frac{B^{2} - 2 A C}{A^{2}}

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\frac{2 A C - B^{2}}{A^{2}}

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\frac{A^{2}}{B^{2} - 2 C}

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Solution

The correct option is C $\frac{2 A C - B^{2}}{A^{2}}$
$A x^{2} + B x + C = 0 r o o t s : r, s r + s = - \frac{B}{A}, r s = \frac{C}{A} x^{2} + p x + q = 0 r o o t s : r^{2}, s^{2} r^{2} + s^{2} = - p, r^{2} \cdot s^{2} = q {(r + s)}^{2} - 2 r s = - p \frac{B^{2}}{A^{2}} - \frac{2 C}{A} = - p ∴ p = \frac{2 A C - B^{2}}{A^{2}}$

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The of roots Ax2+Bx+C=0 are r and s. For the roots of x2+px+q=0 to be r2 and s2, p must equal:

The correct option is C 2AC−B2A2Ax2+Bx+C=0roots:r,sr+s=−BA,rs=CAx2+px+q=0roots:r2,s2r2+s2=−p,r2⋅s2=q(r+s)2−2rs=−pB2A2−2CA=−p∴p=2AC−B2A2

The of roots $A x^{2} + B x + C = 0$ are r and s. For the roots of $x^{2} + p x + q = 0$ to be $r^{2}$ and $s^{2}$ , p must equal: