If a, b and c(a>0, c>0) are in GP, then consider the following in respect of the equation a x^2+b x+c=0 : 1. The equation has imaginary roots. 2. The ratio of the roots of the equation is 1: \omega where \omega is a cube root of unity. 3. The product of roots of the equation is (\frac{b^2}{a^2}). Which of the statements given above are correct?

UPSC NDA I 2024 Mathematics Paper

Question : 32 of 120

Marks: +1, -0

If a,b and c(a>0,c>0) are in GP, then consider the following in respect of the equation ax2+bx+c=0 :
1. The equation has imaginary roots.
2. The ratio of the roots of the equation is 1:ω where ω is a cube root of unity.
3. The product of roots of the equation is (‌

).
Which of the statements given above are correct?

1 and 2 only
2 and 3 only
1 and 3 only
1,2 and 3

Validate

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