I- p 2-7 p -12II- q 2-3 q -2-0A- If p q

The correct option is E If p gt;qEquation I p^2 7p = 12 ⇒ p^2 7p + 12=0 ⇒ p^2 3p 4p+12=0 ⇒ p(p 3) 4(p 3) = 0 ⇒ (p 4)(p 3)=0 ∴ p =3 or 4 Equation II q^2 ...

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Quantitative Aptitude

Quadratic Equations

I. p 2-7 p =-...

Question

I. $p^{2} - 7 p = - 12$
II. $q^{2} - 3 q + 2 = 0$

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 B If $p > q$
Equation I
$p^{2} - 7 p = - 12$
$\Rightarrow p^{2} - 7 p + 12 = 0$
$\Rightarrow p^{2} - 3 p - 4 p + 12 = 0$
$\Rightarrow p (p - 3) - 4 (p - 3) = 0$
$\Rightarrow (p - 4) (p - 3) = 0$
$∴ p = 3$ or $4$

Equation II
$q^{2} - 3 q + 2 = 0$
$\Rightarrow q^{2} - 2 q - q + 2 = 0$
$\Rightarrow q (q - 2) - 1 (q - 2) = 0$
$\Rightarrow (q - 1) (q - 2)$
$∴ q = 1$ or $2$
Hence, p>q

Suggest Corrections

I. p2−7p=−12 II. q2−3q+2=0

The correct option is B If p>qEquation I p2−7p=−12 ⇒p2−7p+12=0 ⇒p2−3p−4p+12=0 ⇒p(p−3)−4(p−3)=0 ⇒(p−4)(p−3)=0 ∴p=3 or 4 Equation II q2−3q+2=0 ⇒q2−2q−q+2=0 ⇒q(q−2)−1(q−2)=0 ⇒(q−1)(q−2) ∴q=1 or 2 Hence, p>q

I. $p^{2} - 7 p = - 12$
II. $q^{2} - 3 q + 2 = 0$