Let `a >0,b >0` and `c >0` . Then, both the roots of the equation `a x^2+b x+c=0` : a. are real and negative b. have negative real parts c. have positive real parts d. None of the above

If a,b, cinR , show that roots of the equation (a-b)x^(2)+(b+c-a)x-c=0 are real and unequal,

If a,b,c,depsilon R and f(x)=ax^3+bx^2-cx+d has local extrema at two points of opposite signs and abgt0 then roots of equation ax^2+bx+c=0 (A) are necessarily negative (B) have necessarily negative real parts (C) have necessarily positive real parts (D) are necessarily positive

If the roots of the equation x^2+2c x+a b=0 are real unequal, prove that the equation x^2-2(a+b)x+a^2+b^2+2c^2=0 has no real roots.

If a, b, c are positive and a = 2b + 3c, then roots of the equation ax^(2) + bx + c = 0 are real for

Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are always a. positive b. real c. negative d. none of these

If the roots of the equation ax^2 + bx + c = 0, a != 0 (a, b, c are real numbers), are imaginary and a + c < b, then

-If a,b,c in R then prove that the roots of the equation 1/(x-a)+1/(x-b)+1/(x-c)=0 are always real cannot have roots if a=b=c

If a and c are the lengths of segments of any focal chord of the parabola y^2=2b x ,(b >0), then the roots of the equation a x^2+b x+c=0 are (a) real and distinct (b) real and equal (c) imaginary (d) none of these

If the equation ax^(2) + bx + c = 0, a,b, c, in R have non -real roots, then

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