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If the roots of the equation ax^(2)+bx+c...

If the roots of the equation `ax^(2)+bx+c=0(a!=0)` be `alpha` and `beta` and those of the equation `Ax^(2)+Bx+C=0(A!=0)` be `alpha+k` and `beta+k`.Prove that
`(b^(2)-4ac)/(B^(2)-4AC)=(a/A)^(2)`

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`:'alpha-beta=(alpha+k)-(beta+k)`
`implies(sqrt(b^(2)-4ac))/a=(sqrt((B^(2)-4AC)))/A[ :' alpha-beta=(sqrt(D))/a]`
`impliessqrt(((b^(2)-4ac)/(B^(2)-4AC)))=(a/A)`
On squaring both sides then we get
`(b^(2)-4ac)/(B^(2)-4AC)=(a/A)^(2)`
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ARIHANT MATHS-THEORY OF EQUATIONS-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. In the quadratic equation ax^2 + bx + c = 0. if delta = b^2-4ac and al...

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  3. Let S denote the set of all polynomials P(x) of degree lt=2 such th...

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  12. If the difference between the roots of the equation x^2+a x+1=0 is les...

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  15. How many real solutions does the equation x^7+14 x^5+16 x^3+30 x-560=0...

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  16. Suppose the cubic x^(3)-px+q has three distinct real roots, where pgt0...

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  17. The smallest value of k, for which both the roots of the equation, x^2...

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  18. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, ...

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  19. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

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  20. Conder the function f(x)=1+2x+3x^2+4x^3 Let the sum of all distinct ...

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  21. Let alpha and beta be the roots of x^2-6x-2=0 with alpha>beta if an=al...

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