The roots of the equation `ax^(2)+bx+c=0` where `a!=0`,are:
1) `(b+-sqrt(b^(2)-4ac))/(2a)`, 2) `(-b+-sqrt(b^(2)-4ac))/(2c)` 3) `(-b+-sqrt(b^(2)-4ac))/(2a)`, 4) `(2a)/(2a-b+sqrt(b^(2)-4ac))`

If the roots of the equation ax^2+bx+c=0 differ by K then b^(2)-4ac=

If the roots of the equation ax^(2)+bx+c=0 differ by K then b^(2)-4ac= O a^(2)k^(2) O ak O a^(2)k O ak^(2)

If alpha,beta are the roots of the equation ax^(2)+bx+c=0, then the value of a alpha^(2)+c/a alpha+b+(a beta^(2)+c)/(a beta+b) is (b(b^(2)-2ac))/(4a) b.(b^(2)-4ac)/(2a) c.(b(b^(2)-2ac))/(a^(2)c) d.none of these

If ratio of the roots of the equation ax^(2)+bx+c=0 is m:n then (A) (m)/(n)+(n)/(m)=(b^(2))/(ac) (B) sqrt((m)/(n))+sqrt((n)/(m))=(b)/(sqrt(ac))],[" (C) sqrt((m)/(n))+sqrt((n)/(m))=(b^(2))/(ac)]

If the roots of the equation ax^(2)+bx+c=0 are of the form (k+1)/k and (k+2)/(k+1), then (a+b+c)^(2) is equal to 2b^(2)-ac b.a62 c.b^(2)-4ac d.b^(2)-2ac

If sintheta and costheta are roots of the equation ax^(2)+bx+c=0 , prove that a^(2)-b^(2)+2ac=0 .

If r is the ratio of the roots of the equation ax^(2)+bx+c=0, then r is the root of the equation.(A) acx^(2)+(2ac-b^(2))x+ac=0 (C) acx^(2)+(2ac-b^(2))x-ac=0 (B) acx^(2)-(2ac-b^(2))x+ac=0(D)acx^(2)-(2ac-b^(2))x-ac=0

If the roots of the equation ax^(2)+2bx+c=0 and -2sqrt(acx)+b=0 are simultaneously real, then prove that b^(2)=ac

The roots of ax^(2)+bx+c=0, ane0 are real and unequal, if (b^(2)-4ac)

Four steps to derive the quadratic formula are shown below . (I) x^(2)+(bx)/a=(-c)/a (II) (x+b/(2a))^(2)=(b^(2)-4ac)/(4a^(2)) (III) x =pm sqrt((b^(2)-4ac)/(4a^(2)))-b/(2a) (IV) x^(2)+(bx)/a +(b/(2a))^(2)=(-c)/a + (b/(2a))^(2) What is the correct order for these steps ?