JIPMAT 2024 (QA) - If the roots of the equation x^2-p x+54=0 are in the ratio 2: 3, then value of p is: | PYQs + Solutions | AfterBoards
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JIPMAT 2024

Algebra
>
Quadratic Equations

Medium

If the roots of the equation x2−px+54=0x^{2}-p x+54=0 are in the ratio 2:32: 3, then value of pp is:

Correct Option: 4
Let the roots be 2k2k and 3k3k where kk is some number
Sum of roots: 2k+3k=−ba=p2k + 3k = \frac{-b}{a} =p \newline Product of roots: (2k)(3k)=ca=54(2k)(3k) = \frac{c}{a} = 54
From product of roots:
6k2=546k^2 = 54
k2=9k^2 = 9
k=±3k = \pm 3
Let us try with k=3k=3: \newline First root =2k=2(3)=6= 2k = 2(3) = 6 \newline Second root =3k=3(3)=9= 3k = 3(3) = 9
p=2k+3k=5k=5(3)=15p = 2k + 3k = 5k = 5(3) = \boxed{15}
Trying k=−3k=-3 would also hold the ratio true.

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