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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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To prove that \( a^4 = b^2(b^2 - 4ac) \) given that \( \tan \theta \) and \( \sec \theta \) are the roots of the quadratic equation \( ax^2 + bx + c = 0 \), we can follow these steps: ### Step 1: Use the relationships for the sum and product of roots For a quadratic equation \( ax^2 + bx + c = 0 \), if \( r_1 \) and \( r_2 \) are the roots, then: - The sum of the roots \( r_1 + r_2 = -\frac{b}{a} \) - The product of the roots \( r_1 \cdot r_2 = \frac{c}{a} \) Here, let \( r_1 = \tan \theta \) and \( r_2 = \sec \theta \). ...
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