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If tanthetaa n dsectheta are the roots o...

If `tanthetaa n dsectheta` are the roots of `a x^2+b x+c=0,` then prove that `a^4=b^2(b^2 - 4ac)dot`

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`tan theta + sec theta = - (b)/(a)` (1)
` tan theta sec theta = (c)/(a)` (2)
Now, `sec^(2) theta - tan^(2) theta = 1`
`rArr sec theta - tan theta = - (a)/(b) ` (3)
From (1) and (3) .
`rArr sec theta = - ((a^(2) + b^(2)))/(2ab) and tan theta = ((a^(2) - b^(2)))/(2ab)`
substituting these values in Eq. (2), we have
`((a^(2) + b^(2))(b^(2) - a^(2)))/(4a^(2)b^(2)) = (c)/(a)`
or `b^(4) - a^(4) = 4acb ^(2)`
or `a^(4) = b^(2)(b^(2) - 4ac)`
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