If \;α and α are the roots of the equation a x²+b x+c=0, then

Correct Answer is : a2−b2+2ac=0a²-b²+2 a c=0a2−b2+2ac=0

Correct Answer is : a2−b2+2ac=0a²-b²+2 a c=0a2−b2+2ac=0

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CGPET 2015 Solved Paper

Section: Mathematics

Question : 137 of 150

Marks: +1, -0

\sin\;\alpha

\cos\alpha

a x^{2}+b x+c=0

Solution:

It is given that, sin α and cos α are the roots of

ax^{2}+bx+c=0

∴ Sum of the roots

= \sin\alpha + \cos\alpha = \frac{-b}{a}

and the product of the roots

= \sin\alpha \times \cos\alpha = \frac{c}{a}

∵

(\sin\alpha + \cos\alpha)^{2} = \sin^{2}\alpha + \cos^{2}\alpha + 2\sin\alpha \cos\alpha

∴

\left(\frac{-b}{a}\right)^{2} = 1+2\left(\frac{c}{a}\right) \quad \left[ \because \sin^{2}\alpha + \cos^{2}\alpha =1 \right]

⇒

\frac{b^{2}}{a^{2}} = \frac{a+2c}{a}

⇒

b^{2} = a(a+2c)

⇒

b^{2}=a^{2}+2ac

⇒

a^{2}-b^{2}+2ac=0

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