If sin alpha and cos alpha are the roots of the equation ax squared + by + c =0. Then prove that a squared + 2ac ='b squared

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first of all equation is wrong because there can't be two variable.

now ax2+bx+c=0

now since sin alpha and cos alpha are the roots therefore

sum of the roots will be

sin alpha + cos alpha = -b/a ......... 1.

sin alpha * cos alpha =c/a ..............2.

now on sqauaring equation 1 we get

(sin alpha + cos alpha)2 = (-b/a)2

sin2 alpha + cos2alpha + 2sin alpha cos alpha= b2/a2

1 + 2c/a=b2/a2

a+2c=ab2/a2

a+2c=b2/a

a(a +2c)=b2

a2+2c=b2.

thus proved ..................

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