If p1 p=2(q1 +q) then which of following statement about the quadratic equations x2 +px+q=0; x2 +p1 x+q1 =0 is always true (Here p, p1 , q, q1 , ∈R )

Δ1+Δ2=p2+p12−4q+q1=p2+p12−2p1p=p−p12≥0Both Δ1,Δ2cannot be negative..

If p1 p=2(q1 +q) then which of following statement about the quadratic equations x2 +px+q=0; x2 +p1 x+q1 =0 is always true (Here p, p1 , q, q1 , ∈R )

Δ1+Δ2=p2+p12−4q+q1=p2+p12−2p1p=p−p12≥0Both Δ1,Δ2cannot be negative..

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If p₁ p=2(q₁ +q) then which of following statement about the quadratic equations x² +px+q=0; x² +p₁ x+q₁ =0 is always true (Here p, p₁ , q, q₁ , $\in$ R )

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at least one of the equations has real roots

Both the equations have real roots

Both the equations have imaginary roots

exactly one of them has equal roots

answer is C.

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$\begin{aligned} Δ_{1} + Δ_{2} = p^{2} + p_{1}^{2} - 4 (q + q_{1}) \end{aligned}$

$= p^{2} + p_{1}^{2} - 2 p_{1} p$

$= {(p - p_{1})}^{2} \geq 0$
Both $Δ_{1}, Δ_{2}$ cannot be negative..

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If p1 p=2(q1 +q) then which of following statement about the quadratic equations x2 +px+q=0; x2 +p1 x+q1 =0 is always true (Here p, p1 , q, q1 , ∈R )

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If p₁ p=2(q₁ +q) then which of following statement about the quadratic equations x² +px+q=0; x² +p₁ x+q₁ =0 is always true (Here p, p₁ , q, q₁ , $\in$ R )