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Quadratic with equal roots: find the parameter

This type of question, asked 2 times: 23 Jan 2025, 3 Apr 2025. All 2 questions below, oldest first.

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  1. Question 1

    23 Jan 2025

    75
    If the equation a(b−c)x2+b(c−a)x+c(a−b)=0a(b-c)x^{2}+b(c-a)x+c(a-b)=0 has equal roots, where a+c=15a+c=15 and b=365b=\frac{36}{5}, then a2+c2a^{2}+c^{2} is equal to

  2. Question 2

    3 Apr 2025

    132
    Let the equation x(x+2)(12−k)=2x(x+ 2)(12 -k) = 2 have equal roots. Then the distance of the point (k,k2)\left( k,\frac{k}{2} \right) from the line 3x+4y+5=03x+ 4y+ 5 = 0 is.

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