I- p2-12 p-35-0II- 2 q 2-22 q -56-0A- If pqC- If p - qD- If p-qE- If p - q

The correct option is E If p ≤ qEquation I p^2+12p+35=0 ⇒ p^2+7p+5p+35=0 ⇒ p(p+7)+5(p+7)=0 ⇒ (p+7)(p+5)=0 ∴ p = 5 or 7 Equation II 2q^2 +22q+56=0 ⇒ 2q^2+14q ...

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Quantitative Aptitude

Quadratic Equations

I. p2+12 p+35...

Question

I. $p^{2} + 12 p + 35 = 0$
II. $2 q^{2} + 22 q + 56 = 0$

p < q

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p > q

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p \leq q

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p \geq q

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p = q

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Solution

The correct option is C If $p \leq q$
Equation I
$p^{2} + 12 p + 35 = 0$
$\Rightarrow p^{2} + 7 p + 5 p + 35 = 0$
$\Rightarrow p (p + 7) + 5 (p + 7) = 0$
$\Rightarrow (p + 7) (p + 5) = 0$
$∴ p = - 5$ or $- 7$

Equation II
$2 q^{2} + 22 q + 56 = 0$
$\Rightarrow 2 q^{2} + 14 q + 8 q + 56 = 0$
$\Rightarrow 2 q (q + 7) + 8 (q + 7) = 0$
$\Rightarrow (q + 7) (2 q + 8) = 0$
$\Rightarrow q = - 7, - 4$
Hence, $p \leq q$

Suggest Corrections

I. p2+12p+35=0 II. 2q2+22q+56=0

The correct option is C If p≤qEquation I p2+12p+35=0 ⇒p2+7p+5p+35=0 ⇒p(p+7)+5(p+7)=0 ⇒(p+7)(p+5)=0 ∴p=−5 or −7 Equation II 2q2+22q+56=0 ⇒2q2+14q+8q+56=0 ⇒2q(q+7)+8(q+7)=0 ⇒(q+7)(2q+8)=0 ⇒q=−7,−4 Hence, p≤q

I. $p^{2} + 12 p + 35 = 0$
II. $2 q^{2} + 22 q + 56 = 0$