If sin- and cos- are the roots of the equation ax 2- bx - c -0- thenA- a2-b2-2 a c-0B- a-c2-b2-c2C- a2-b2-2 a c-0D- a-c2-b2-c2

The correct option is A a2 b2 + 2ac = 0Sum of the roots = b/a Product of the roots = b/a sin α + cos α = b/a.......(1) sin α× cos α = c/a.......(2) Squar ...

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Standard X

Mathematics

Roots of Quadratic Equation

If sinα and c...

Question

If sin α and cos α are the roots of the equation $a x^{2} + b x + c = 0,$ then

a² - b² + 2ac = 0

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(a - c)² = b² + c²

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a² + b² + 2ac = 0

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(a - c)² = b² - c²

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Solution

The correct option is A
a² - b² + 2ac = 0

Sum of the roots = $- \frac{b}{a}$
Product of the roots = $\frac{b}{a}$
$s i n α + c o s α = - \frac{b}{a} . . . . . . . (1) s i n α \times c o s α = \frac{c}{a} . . . . . . . (2) S q u a r i n g (1) g i v e s (s i n α + c o s α)^{2} = {(- \frac{b}{a})}^{2} (s i n α)^{2} + (c o s α)^{2} + 2 s i n α \times c o s α = {(\frac{b}{a})}^{2} \Rightarrow 1 + 2 \times (\frac{c}{a}) = {(\frac{b}{a})}^{2} M u l t i p l y i n g w i t h a^{2} g a v e s a^{2} + 2 a c = b^{2} \Rightarrow a^{2} - b^{2} + 2 a c = 0$

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If sin α and cos α are the roots of the equation ax2+bx+c=0, then

If sin α and cos α are the roots of the equation $a x^{2} + b x + c = 0,$ then