Question

Let alpha₁,alpha₂ and beta₁,beta₂ be the roots of ax²+bx+c=0 and px²+qx+r=0 respectively. If the system alpha₁ y+alpha₂ z=0, beta₁ y+beta₂ z=0 has a non-trivial solution, then

• A. \(\dfrac{b^2}{q^2}=\dfrac{ac}{pr}\)
• B. \(\dfrac{c^2}{r^2}=\dfrac{ab}{pq}\)
• C. \(\dfrac{a^2}{p^2}=\dfrac{bc}{qr}\)
• D. None of these

Hint:

Non-trivial solutions of homogeneous equations require determinant =0.

Answer 1

The Correct Option is A

For non-trivial solution: alpha₁beta₂-alpha₂beta₁=0 Using properties of roots: alpha₁alpha₂=(c)/(a), beta₁beta₂=(r)/(p) Simplifying leads to: (b²)/(q²)=(ac)/(pr)