I- p 2-8 p -15-0II- q 2-5 q -6A- If pqC- If p - qD- If p - qE- If p-q

The correct option is D If p ≥ qEquation I p^2 8p+15=0 ⇒ p^2 3p 5p+15=0 ⇒ p(p 3) 5(p 3)=0 ⇒ (p 3)(p 5)=0 ∴ p = 3 or 5 Equation II q^2 5q= 6 ⇒ q^2 5q+6=0 ⇒ q^2 ...

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Quantitative Aptitude

Equations

I. p 2-8 p +1...

Question

I. $p^{2} - 8 p + 15 = 0$
II. $q^{2} - 5 q = - 6$

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 D If $p \geq q$
Equation I
$p^{2} - 8 p + 15 = 0$
$\Rightarrow p^{2} - 3 p - 5 p + 15 = 0$
$\Rightarrow p (p - 3) - 5 (p - 3) = 0$
$\Rightarrow (p - 3) (p - 5) = 0$
$∴ p = 3$ or $5$

Equation II
$q^{2} - 5 q = - 6$
$\Rightarrow q^{2} - 5 q + 6 = 0$
$\Rightarrow q^{2} - 3 q - 2 q + 6 = 0$
$\Rightarrow q [q - 3] - 2 [q - 3] = 0$
$\Rightarrow [q - 3] [q - 2] = 0$
$\Rightarrow q = 3$ or $2$
Hence, $p \geq q$

Suggest Corrections

I. p2−8p+15=0 II. q2−5q=−6

The correct option is D If p≥qEquation I p2−8p+15=0 ⇒p2−3p−5p+15=0 ⇒p(p−3)−5(p−3)=0 ⇒(p−3)(p−5)=0 ∴p=3 or 5 Equation II q2−5q=−6 ⇒q2−5q+6=0 ⇒q2−3q−2q+6=0 ⇒q[q−3]−2[q−3]=0 ⇒[q−3][q−2]=0 ⇒q=3 or 2 Hence, p≥q

I. $p^{2} - 8 p + 15 = 0$
II. $q^{2} - 5 q = - 6$