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✨1
➡️ One contains 850 litres.
Another contains 680 litres.
➡️ Now, H. C. F of 850 and 680 is
= 170
➡️
✨19
➡️ We know that the constant term is the multiplication of the roots.
➡️ So, when it is 0, the multiplication of the roots is 0.
➡️ Hence, one of the roots is 0.
✨20
➡️ Coefficient of x is the sum of the roots.
➡️ When, coefficient of x is 0, Hence, the sum of the roots is 0.
➡️ Thus, the roots are equal in magnitude but with opposite signs.
✨21
➡️ Let, x and 3x.
➡️ 3x * x = 27.
Or, 3x^2 = 27
Or, x = 3.
And 3x = 9.
➡️ So, k = sum of roots
= 9 + 3 = 12.
✨22
➡️ Let, 2x and 3x.
➡️ 2x + 3x = 15
Or, x = 2.
➡️ 2x = 6 and 3x = 9.
➡️ Hence, the equation will be
= a^2 + a(6 + 9) + 6 * 9
= a^2 + 15x + 54.
That's it..
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