Let alpha , beta be the roots of x^2-x+p...

Let `alpha` , `beta` be the roots of `x^2-x+p=0 and gamma,delta` be the roots of `x^2-4x+q=0 `. If `alpha,beta,gamma` are in GP , then the integer values of p and q respectively are:

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Let alpha,beta be the roots of the equation x^2-4x+A=0 and gamma,delta be the roots of the equation x^2-36x+B=0 . If alpha,beta,gamma and delta are In G.P. having positive common ratio, find the value of A and B.

Let alpha,beta be the roots of the equation x^2-3x+a=0 and gamma,delta the roots of the equation x^2-12x+b=0 . If alpha,beta,gamma and delta are in G.P. having positive common ratio, then find the values of a and b.

If alpha,beta are the roots of x^2-px+1=0 and gamma is a root of x^2+px+1=0 , then (alpha+gamma)(beta+gamma) is

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Let alpha_1,beta_1 be the roots x^2-6x+p=0a n d alpha_2,beta_2 be the roots x^2-54 x+q=0dot If alpha_1,beta_1,alpha_2,beta_2 form an increasing G.P., then sum of the digits of the value of (q-p) is ___________.

If alpha,beta are the roots x^2+px+q =0 and gamma,delta are the roots of x^2+rx+s =0, evaluate (alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta) in terms of p,q,r and s. Deduce the condition that the equation may have a common root.

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If alpha,beta are roots of x^2+p x+1=0a n dgamma,delta are the roots of x^2+q x+1=0 , then prove that q^2-p^2=(alpha-gamma)(beta-gamma)(alpha+delta)(beta+delta) .

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions

Let alpha,beta be the roots of the quadratic equation a x^2+b x+c=0 an...
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Let z, omega be complex numbers such that barz+ibaromega=0 and arg(z o...
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For any two complex numbers z1 and z2, , prove that Re (z1 z2) = Re ...
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Let z1 and z2 be complex numbers such that z1 nez2 and absz1=absz2 if ...
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The equation sqrt(x+1)-sqrt(x-1)=sqrt(4x-1) has
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A value of b for which the equations x^2+bx-1=0, x^2+x+b =0 have one r...
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